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Algebra 1 : Algebra 1

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Example Questions

Example Question #39 : Monetary Percentage

Food Plus is advertising two-liter bottles of Delicious Soda for $1.69 each. They are also advertising two-liter bottles of Tasty Soda for $1.89 each, or three for $4.50.

Randy wants to purchase twelve two-liter bottles of soda. He does not care whch brand he purchases, since he thinks they taste the same. Taking into account the fact that the rate of sales tax is 7%, which brand of soda can Randy purchase more cheaply, and how much will he save?

Possible Answers:

The Delicious Soda costs $2.40 less

Insufficient information is given to answer the question

The Tasty Solda costs $2.44 less

The Tasty Solda costs $2.28 less

The Delicious Soda costs $2.57 less

Correct answer:

The Tasty Solda costs $2.44 less

Explanation:

How to calculate the amount of sales tax?

Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
Add the sales tax value to the pre-tax value to calculate the total cost.

Calculating sales tax at time of purchase:

In order to calculate the sales tax of an item, we need to first multiply the pre-tax cost of the item by the sales tax percentage after it has been converted into a decimal. Once the sales tax has been calculated it needs to be added to the pre-tax value in order to find the total cost of the item. Let's start by working with an example. If a magazine costs $2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

$6\% \rightarrow 0.06$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.06\times\$2.35$

$\textup{Sales tax}=\$0.141$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$0.14$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$2.35+\$0.14$

$\textup{Total cost}=\$2.49$

Calculating the sales tax percentage of a total:

If we are given the total cost of an item or group of items and the pre-tax cost of the good(s), then we can calculate the sales tax percentage of the total cost. First, we need to subtract the pre-tax value from the total cost of the purchase. Next, we need to create a ratio of the sales tax to the pre-tax cost off the items. Last, we need to create a proportion where the pre-tax cost is related to 100% and solve for the percentage of the sales tax. Let's start by working through an example. If a person pays $245.64 for groceries that cost $220.00 pre tax, then what is the sales tax percentage for the items.

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

$\textup{Sales tax}=\textup{Total cost}-\textup{Pre-tax value}$

$\textup{Sales tax}=\$245.64-\$220.00$

$\textup{Sales tax}=\$25.64$

Next, create a ratio of the sales tax to the pre-tax cost of the items.

$\frac{\textup{Sales tax}}{\ \textup{Pre-tax value}} = \frac{\$25.64}{\$220.00}$

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

$\frac{\$25.64}{\$220.00}=\frac{\textup{Sales tax percentage}}{100\%}$

Cross multiply and solve.

$\$220.00\times\textup{Sales tax percentage}=\$25.64\times 100\%$

$\$220.00\times\textup{Sales tax percentage}=\$2564.00$

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

$\frac{\$220.00\times\textup{Sales tax percentage}}{\$220.00}=\frac{\$2564.00}{\$220.00}$

$\textup{Sales tax percentage}=11.6545455\%$

Round to two decimal places since our answer is in dollars and cents.

$\textup{Sales tax percentage}=11.65\%$

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

$11.6545455\% \rightarrow 0.116545455$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.116545455\times\$220.00$

$\textup{Sales tax}=\$25.6400001$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$25.64$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$220.00+\$25.64$

$\textup{Total cost}=\$245.64$

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

Solution:

12 bottles of Delicious Soda will cost

$12 \times \$ 1.69 = \$20.28$

The sales tax is 7% of this, or

$\$20.28 \times 0.07 = \$ 1.42$

After tax, the cost is

$\$20.28 + \$ 1.42 = \$21.70$

12 bottles of Tasty Soda will be purchased at the three-for-$4.50 rate, so they will cost

$\frac{12}{3} \times \$ 4 .50= \$ 18.00$

The sales tax is 7% of this, or

$\$18.00 \times 0.07 = \$ 1.26$

After tax, the cost is

$\$ 18.00 + \$1.26 = \$19.26$

This makes the Tasty Soda less expensive by

$\$21.70 - \$19.26 = \$ 2.44$

Report an Error

Example Question #40 : Monetary Percentage

Sandy wants to buy a pair of shoes in one of two stores. Simon's, which is in her own state, charges $150, plus 6% sales tax. Garfunkel's, which is just across the border in another state, charges $175, and no sales tax. In which store would the shoes be cheaper, and by how much?

Possible Answers:

She would save $14.50 by going to Garfunkel's

She would save $16 by going to Simon's

She would save $16 by going to Garfunkel's

She would save $14.50 by going to Simon's

She would pay the same amount regarless of what store she chose

Correct answer:

She would save $16 by going to Simon's

Explanation:

How to calculate the amount of sales tax?

Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
Add the sales tax value to the pre-tax value to calculate the total cost.

Calculating sales tax at time of purchase:

$6\% \rightarrow 0.06$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.06\times\$2.35$

$\textup{Sales tax}=\$0.141$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$0.14$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$2.35+\$0.14$

$\textup{Total cost}=\$2.49$

Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

$\textup{Sales tax}=\textup{Total cost}-\textup{Pre-tax value}$

$\textup{Sales tax}=\$245.64-\$220.00$

$\textup{Sales tax}=\$25.64$

Next, create a ratio of the sales tax to the pre-tax cost of the items.

$\frac{\textup{Sales tax}}{\ \textup{Pre-tax value}} = \frac{\$25.64}{\$220.00}$

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

$\frac{\$25.64}{\$220.00}=\frac{\textup{Sales tax percentage}}{100\%}$

Cross multiply and solve.

$\$220.00\times\textup{Sales tax percentage}=\$25.64\times 100\%$

$\$220.00\times\textup{Sales tax percentage}=\$2564.00$

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

$\frac{\$220.00\times\textup{Sales tax percentage}}{\$220.00}=\frac{\$2564.00}{\$220.00}$

$\textup{Sales tax percentage}=11.6545455\%$

Round to two decimal places since our answer is in dollars and cents.

$\textup{Sales tax percentage}=11.65\%$

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

$11.6545455\% \rightarrow 0.116545455$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.116545455\times\$220.00$

$\textup{Sales tax}=\$25.6400001$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$25.64$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$220.00+\$25.64$

$\textup{Total cost}=\$245.64$

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

Solution:

Simon's charges $150 plus 6% tax, or

$\$ 150 +\$ 150 \times 6 \%$

$= \$150 +\$ 150 \times 0.06$

$= \$ 150 + \$ 9$

$= \$ 159$

Garfunkel's would charge $175, but without sales tax. Nonetheless, Sandy would pay

$\$175 - \$ 159 = \$ 16$

more by going to Garfunkel's.

Report an Error

Example Question #41 : Monetary Percentage

A bike before sales tax cost $60. What is the sales tax if the rate is 8 percent?

Possible Answers:

$\$55.20$

$\$12$

$\$48$

$\$0.48$

$\$4.80$

Correct answer:

$\$4.80$

Explanation:

How to calculate the amount of sales tax?

Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
Add the sales tax value to the pre-tax value to calculate the total cost.

Calculating sales tax at time of purchase:

$6\% \rightarrow 0.06$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.06\times\$2.35$

$\textup{Sales tax}=\$0.141$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$0.14$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$2.35+\$0.14$

$\textup{Total cost}=\$2.49$

Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

$\textup{Sales tax}=\textup{Total cost}-\textup{Pre-tax value}$

$\textup{Sales tax}=\$245.64-\$220.00$

$\textup{Sales tax}=\$25.64$

Next, create a ratio of the sales tax to the pre-tax cost of the items.

$\frac{\textup{Sales tax}}{\ \textup{Pre-tax value}} = \frac{\$25.64}{\$220.00}$

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

$\frac{\$25.64}{\$220.00}=\frac{\textup{Sales tax percentage}}{100\%}$

Cross multiply and solve.

$\$220.00\times\textup{Sales tax percentage}=\$25.64\times 100\%$

$\$220.00\times\textup{Sales tax percentage}=\$2564.00$

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

$\frac{\$220.00\times\textup{Sales tax percentage}}{\$220.00}=\frac{\$2564.00}{\$220.00}$

$\textup{Sales tax percentage}=11.6545455\%$

Round to two decimal places since our answer is in dollars and cents.

$\textup{Sales tax percentage}=11.65\%$

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

$11.6545455\% \rightarrow 0.116545455$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.116545455\times\$220.00$

$\textup{Sales tax}=\$25.6400001$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$25.64$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$220.00+\$25.64$

$\textup{Total cost}=\$245.64$

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

Solution:

Multiply the sales percentage with the cost of the bike before sales tax. This will determine the amount of tax the buyer must pay.

A percent is a number out of 100 parts.

Multiply the price with the percent.

$\$60 \cdot \frac{8}{100} = \frac{480}{100} = \$4.80$

The tax on the bike is: $\$4.80$

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Example Question #41 : How To Find The Amount Of Sales Tax

Carol buys some shoes with a sticker price of $80.00. In the city where Carol lives, the state sales tax is 7.5% and the city sales tax is an additional 0.5%. How much will Carol pay in tax at checkout?

Possible Answers:

$\$0.64$

$\$6.40$

$\$8.00$

$\$3.00$

$\$0.80$

Correct answer:

$\$6.40$

Explanation:

How to calculate the amount of sales tax?

Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
Add the sales tax value to the pre-tax value to calculate the total cost.

Calculating sales tax at time of purchase:

$6\% \rightarrow 0.06$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.06\times\$2.35$

$\textup{Sales tax}=\$0.141$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$0.14$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$2.35+\$0.14$

$\textup{Total cost}=\$2.49$

Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

$\textup{Sales tax}=\textup{Total cost}-\textup{Pre-tax value}$

$\textup{Sales tax}=\$245.64-\$220.00$

$\textup{Sales tax}=\$25.64$

Next, create a ratio of the sales tax to the pre-tax cost of the items.

$\frac{\textup{Sales tax}}{\ \textup{Pre-tax value}} = \frac{\$25.64}{\$220.00}$

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

$\frac{\$25.64}{\$220.00}=\frac{\textup{Sales tax percentage}}{100\%}$

Cross multiply and solve.

$\$220.00\times\textup{Sales tax percentage}=\$25.64\times 100\%$

$\$220.00\times\textup{Sales tax percentage}=\$2564.00$

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

$\frac{\$220.00\times\textup{Sales tax percentage}}{\$220.00}=\frac{\$2564.00}{\$220.00}$

$\textup{Sales tax percentage}=11.6545455\%$

Round to two decimal places since our answer is in dollars and cents.

$\textup{Sales tax percentage}=11.65\%$

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

$11.6545455\% \rightarrow 0.116545455$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.116545455\times\$220.00$

$\textup{Sales tax}=\$25.6400001$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=\$25.64$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=\$220.00+\$25.64$

$\textup{Total cost}=\$245.64$

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

Solution:

Find the tax () by multiplying the retail price by the total sales tax rate.

Start by converting the state and city sales tax percentages into decimals:

$7.5\% = 0.075$

$0.5\% = 0.005$

Then set up the equation as follows:

$t=80\cdot (0.075+0.005)$

$\ t=6.4$

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Example Question #1 : How To Find Simple Interest

A bank account begins at $175, and it earns 15% interest. The accound holder then takes 76% of the available balance out. How much money is left in the bank account?

Possible Answers:

$\$201.25$

$\$125.25$

$\$49.50$

$\$48.30$

$\$76.67$

Correct answer:

$\$48.30$

Explanation:

The account begins at $175 and then earns 15% interest:

$175\cdot 1.15=201.25$

If the account owner takes out 76% of the available balance, that means that 24% off the account will be remaining:

$201.25\cdot 0.24=48.3$

$48.30 remains

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Example Question #1 : How To Find Simple Interest

Exactly one year ago, John placed $8,000 into an investment account. Over the past year, the investments in his account have increased in value by 12%. How much money does he have now?

Possible Answers:

8880

8840

8920

9000

8960

Correct answer:

8960

Explanation:

John started out with $8,000 and increased it by 12% after a year. This indicates that by the end of the year, he has 112% of $8,000 (The original $8,000 plus the 12% return from his investments). Convert 112% into its decimal equivalent of 1.12 and multiply it by $8,000 to get John's current savings amount:

1.12*8000=8960

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Example Question #3 : How To Find Simple Interest

You borrow $800 from a friend and your friend charges you a simple interest of 8% at an annual rate. Assume that you don't pay any of it back, how much interest will you owe in three years?

Possible Answers:

$\$183$

$\$192$

$\$158$

$\$234$

$\$212$

Correct answer:

$\$192$

Explanation:

The formula for simple interest is

i=prt

where is the amount that's loaned to you, is the annual interest rate, and is the time (in years) interest accumulates. In this problem,

p=800

$r=8\ percent=.08$

and

t=3

Plug these values in:

i=(800)(0.08)(3)

i=192

So in three years, you will owe an interest of $192.

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Example Question #3 : How To Find Simple Interest

Jennifer has invested her money in an account that yields 5% interest per year. If she invested $12,000, how much interest will she yield?

Possible Answers:

$\$600$

$\$60$

$\$700$

$\$6000$

Correct answer:

$\$600$

Explanation:

To solve this, multiply 12,000 by the decimal equivalent of 5% (.05). This gives a total interest of $600.

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Example Question #1 : How To Find Simple Interest

You take a loan of $5,000 from your bank to buy a car. Your bank charges you interest at an annual rate of 3.5%. How much interest will you accrue in three years, assuming that you haven't paid any of the principal back? (Use simple interest, not compound.)

Possible Answers:

$\$745$

$\$575$

$\$625$

$\$525$

$\$900$

Correct answer:

$\$525$

Explanation:

The formula in calculating interest is

i=prt ,

where is the principal, is the annual interest rate in decimal form, and is number of years the principal accrues interest. In this problem, p=5000 , r=0.035 , and t=3 .

To find the interest, plug these values into the equation:

i=(5000)(0.035)(3)

i=525

Therefore the accrued interest is $525.

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Example Question #6 : How To Find Simple Interest

If you deposit $\$2500$ into a savings account that yields 5% annual interest, how much interest will you earn in years?

Possible Answers:

$\$375$

$\$3750$

$\$300$

$\$575$

$\$37,500$

Correct answer:

$\$375$

Explanation:

When finding simple interest, we use the following formula:

$\text{Simple Interest (I)} = \text{Principal (P)} \cdot \text{Rate (R)} \cdot \text{Time (T)}$

The principal (P) equals the amount we deposit or invest. In this case,

P = 2500

The rate (R) is the percentage rate at which the principal increases or decreases. In this case,

R = 0.05

because we must convert 5% into decimal form.

The time (T) equals the number of years the money is accruing interest. In the case,

T = 3

So, according to the formula above

$I = P \cdot R \cdot T$

$I = 2500 \cdot 0.05 \cdot 3$

I = 375

Therefore, the total interest earned is $375.

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #39 : Monetary Percentage

How to calculate the amount of sales tax?

Calculating sales tax at time of purchase:

Calculating the sales tax percentage of a total:

Solution:

Example Question #40 : Monetary Percentage

How to calculate the amount of sales tax?

Calculating sales tax at time of purchase:

Calculating the sales tax percentage of a total:

Solution:

Example Question #41 : Monetary Percentage

How to calculate the amount of sales tax?

Calculating sales tax at time of purchase:

Calculating the sales tax percentage of a total:

Solution:

Example Question #41 : How To Find The Amount Of Sales Tax

How to calculate the amount of sales tax?

Calculating sales tax at time of purchase:

Calculating the sales tax percentage of a total:

Solution:

Example Question #1 : How To Find Simple Interest

Example Question #1 : How To Find Simple Interest

Example Question #3 : How To Find Simple Interest

Example Question #3 : How To Find Simple Interest

Example Question #1 : How To Find Simple Interest

Example Question #6 : How To Find Simple Interest

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