How to find the part from the whole with percentage - ISEE Middle Level Quantitative Reasoning

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Question

Sally painted 11 pictures on Monday, 7 pictures on Wednesday, and 3 pictures on Friday. On average, how many pictures did Sally paint on those 3 days?

Answer

To solve, first find the total number of pictures painted:

$\small 11 + 7+ 3= 21$

Then, divide the total number of pictures by the total number of days to find the average.

$\small \small 21\div 3= 7$

Sally painted an average of 7 pictures per day.

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Question

is of what number?

Answer

If is of a number, , then we can set up an equation. First, we convert to a decimal, . Then, we can formulate the equation below.

Solve for by dividing both sides of the equation by .

$\frac{0.125N}{0.125}=\frac{65}{0.125}$

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Question

Which is larger?

a. 10% of 90

b. 5% of 160

c. 20% of 50

d. 30% of 40

Answer

First find the percentage amount for each choice by multiplying the number by the percentage amount

a. $90\ast .10=9$

b. $160\ast .5=8$

c. $50\ast .20=10$

d. $40 \ast .30= 12$

Then compare the amounts to find the largest.

The answer is (d) 12.

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Question

A laptop computer is on sale for 40% less than the original price. If the original price is \$345.00, what is the laptop's current sale price?

Answer

First, multiply the original price by the sale percentage:

Then, subtract that amount from the original price to get the sale price:

.

The laptop's current sale price is $\$ 207.00$

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Question

Helen wants to buy a dress for a party. It is on sale for 37% off. How much does the dress currently costs, if its original price was \$45.00?

Answer

First, multiply 45 by 0.37:

Then, subtract that amount from 45.00 to find the sale price:

Answer: The dress' sale price is \$28.35.

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Question

A restaurant is having a sale and lowering their prices by 20%. If an average meal for two normally costs \$62.00, what will it costs under the current sale?

Answer

Multiply:

Then, subtract that amount from the original price:

Answer: \$49.60

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Question

To get on the ballot for student body president, a student must turn in a petition with the signatures of 4% of the students. If there are 3,268 students, how many signatures must a student get to be on that ballot? (Round to the nearest whole person.)

Answer

4% of 3,268 can be calculated by multiplying 3,268 by 0.04, the decimal equivalent of 4%:

$3,268 \times 0.04 = ?$

Multiply 3,268 by 4, then move the decimal point two places to the right:

$3,268 \times 4 =13,072$ ,

so

$3,268 \times 0.04 = 130.72$

Rounded to the nearest whole number - 131 signatures.

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Question

Candy bought a sweater and a beanie on sale for 20% off. If the sweater cost $ $\small \$45$ and the beanie cost $ $\small 12$ , how much did Candy spend?

Answer

In order to find how much money Candy spent, we must first figure out the cost of the merchandise before the discount. We do this by adding the prices together.

$\small 45+12=57$

Next we must find 20% of \$57.00.

$\small .20\cdot 57=11.40$

Since 20% is the percentage Candy saved, we must subtract \$11.40 from the original price.

$\small 57-11.4=45.60$

So Candy spent \$45.60.

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Question

200 percent of what number is equal to the difference between 75 and 25?

Answer

We must first start by finding the difference between $\small 75$ and $\small 25$ :

$\small 75-25 = 50$

Next find the decimal equivalent of $\small 200$ %, which is done by dividing by $\small 100$ :

$\small 200/100 = 2$

Now we divide $\small 50$ by $\small 2$ .

$\small 50/2 = 25$

Our final answer is $\small 25$ , because when it is multiplied by $\small 200$ %, it equals the difference between $\small 75$ and $\small 25$ .

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Question

75 is 60% of what number?

Answer

Set up the proportion statement and solve for by cross-multiplying:

$\frac{75}{N}= \frac{60}{100}$

$N \cdot 60 = 75 \cdot 100 = 7,500$

$N \cdot 60 \div 60 = 7,500\div 60$

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Question

What is 120% of 120?

Answer

Rewrite 120% as a decimal by writing 120 with a decimal point, then shifting it two spaces left:

Multiply this by 120:

$120 \times 1.2 = 144$

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Question

What is 225% of 225?

Answer

Rewrite 225% as a decimal by writing 225 with a decimal point, then shifting it two spaces left:

Multiply this by 225:

$225 \times 2.25= 506.25$

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Question

What is 77% of 77?

Answer

Rewrite 77% as a decimal by writing 77 with a decimal point, then shifting it two spaces left:

Multiply this by 77:

$77 \times 0.77 = 59.29$

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Question

Jerry buys groceries that cost \$43.23 before tax. The tax on groceries in his locality is 5.5%. He hands the cashier a \$100 bill. What will he get back in change?

Answer

The tax on \$43.23 worth of groceries is 5.5% of that, which is 0.055 multiplied by that:

$\$43.23 \times 0.055 \approx \$ 2.38$ when rounded to the nearest cent.

Add that to the price:

$\$43.23 + $ 2.38 = $45.61$

And subtract that from \$100:

$\$100.00 - $45.61 = $54.39$ , which is the change

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Question

A bicycle Carly wants to buy costs \$250 in her hometown in Tennessee, where she would pay no sales tax. Just across the border in Kentucky, she can buy the same bicycle for \$225 in a store, but the sales tax is 8%. How much would Carly save by buying the bicycle in Kentucky?

Answer

In the Kentucky store, Carly would pay \$225, plus 8% of that amount, in tax; this is:

$\$ 225 +$ 225 \times 0.08 = $ 225 + $ 18 = $243$

She would save $$ 250 - $243 = \$7$

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Question

At the store where Harry works, a hat he wants to buy sells for \$72.00. He gets an employee discount of 20%, and he wants to hold out for two weeks, when the hat is marked down 15%. How much will he be able to buy the hat for then?

Answer

A 20% employee discount means that Harry gets to buy merchandise for 80% of the purchase price. A 15% markdown means that the hat will sell for 85% of its normal price. Therefore, Harry will pay 80% of 85% of \$72 for the hat, or:

$0.8 \times 0.85 \times \$72.00= \$48.96$

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Question

Donald makes \$17.50 an hour at current, and is due for a 5% raise. Also, as a result of an agreement with the union, management has promised a 16% increase in wages across the board for all workers. What will Donald earn per hour after these two increases?

Answer

As a result of a 5% raise, Donald's wages will be 105% of what they were before; the 16% wage hike will make Donald's wages 116% of that. Therefore, Donald will make:

$1.05 \times 1.16 \times 17.50 = $ 21.315 \approx $21.32$

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Question

In appreciation for a job well done, Clark is being awarded a bonus equal to 12.5% of the salary he earned over the last two years. His monthly salary over that period has remained constant at \$4,500 per month. What is the amount of the bonus?

Answer

Over two years, or 24 months, Clark has earned

$$4,500 \times 24 = $108,000$

His bonus is 12.5% of this, or:

$$108,000 \times 0.125 = $13,500$

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Question

What is 40% of $\frac{2}{5}$ ?

Answer

Set up the percent proportion, where is the part:

$\frac{N}{(\frac{2}{5})} = \frac{40}{100}$

Solve for , rewriting as follows:

$N \div \frac{2}{5} = \frac{40\div 20}{100\div 20}$

$N \cdot \frac{5}{2} = \frac{2}{5}$

$N \cdot \frac{5}{2} \div \frac{5}{2} = \frac{2}{5} \div \frac{5}{2}$

$N = \frac{2}{5} \cdot \frac{2} {5} = \frac{4}{25}$

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Question

What is $\frac{1}{6} %$ of 3,000?

Answer

Set up a proportion, as follows:

$\frac{N}{3,000} = \frac{\frac{1}{6}}{100}$

Solve for by cross-mutiplying:

$100 \cdot N = \frac{1}{6} \cdot 3,000$

$100 \cdot N = \frac{1}{6} \cdot\frac{ 3,000}{1}$

$100 \cdot N = 500$

$100 \cdot N \div 100 = 500 \div 100$

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