All ACT Math Resources
Example Questions
Example Question #1231 : Act Math
What is of of ?
For percentage problems, the easiest way to start is by remembering that the word "of" is best translated as a multiplication, while the word "is" is best translated by an equals sign. Thus, for the information provided, we can write the equation:
Solving for , you get:
Alternatively you could first calculate of , which is , and then calculate of that, and you would arrive at the same answer.
Example Question #171 : Arithmetic
A computer originally sold for dollars. Its price was reduced by and then again by . What was the final sale price for the computer? Round to the nearest cent.
The most common way to do a problem like this is to begin by applying the first discount, calculating the amount to be removed from the original price. This is done by multiplying the original price by . This gives you . This is then subtracted from to give you . Once again, this new number is multiplied, now by . This gives you . When subtracted from , this gives you a final price of , or the rounded value of .
A simpler way to do this is to realize that the first price reduction makes the new price to be of the original. The second will then make the price to be of the intermediary price. Thus, you could easily compute:
Example Question #1241 : Act Math
A pound man has a body composition made up of pounds of fat, pounds of muscle, and the rest of other organs, fluid, etc. What is the percentage of his muscle composition (in comparison with his toal weight) if he increases his weight in body fat by ? Round to the nearest hundredth of a percent.
As of right now, the man has pounds of body fat. If this increases by , we he will gain or more pounds of body fat. This means that he will have a total of pounds of body fat. Also, it means that his total weight will be pounds. Therefore, his muscle, as a percent of his total weight will be:
or
Example Question #81 : Percentage
What is of ?
If necessary, round to the nearest percentage.
To calculate the percentage of a percent, convert both percentages to decimals and multiply:
Example Question #81 : Percentage
What percentage of is ? Round your answer to the nearest whole percentage.
To find what percentage is of simply divide by . Thus we see that
Example Question #175 : Arithmetic
If Abraham’s collection in July is 40% of his collection at the end of December, how many stamps must have he obtained in December?
Abraham’s collection in July is 97 stamps. If that is 40% of his collection at the end of the year, his album must have stamps.
Thus, he would have to get stamps to have that happen.
Example Question #1 : How To Find The Amount Of Sales Tax
Beth purchased $21.25 worth of groceries. The sales tax rate is 7.5%. What was her total bill?
$21.93
$23.41
$22.84
$22.11
$23.79
$22.84
The tax is calculated by 0.075 * 21.25 = 1.59375 or $1.59. So the total bill is the cost of items purchased plus tax, which is $21.25 + $1.59 = $22.84.
Example Question #1 : Sales Tax
The last week of August is tax-free week. If the standard tax rate is 8.25%, how much money would a shopper save buying a $50 dress and a $30 pair of shoes during tax free week?
$2.47
$8.00
$7.25
$6.60
$4.13
$6.60
Tax = Total Cost * 0.0825 = (50 + 30) * 0.0825 = (80) x 0.0825 = 6.6 = $6.60
Example Question #1 : How To Find The Amount Of Sales Tax
If a stick of deodorant costs $4.29 with a sales tax of 8.75%. What will the total cost of the item be?
(round to the nearest cent)
$6.47
$4.66
$4.37
$4.76
$4.67
$4.67
To solve for the tax charged multiply 0.0875 by the sales price of $4.29.
This is $0.375375. Add this to the original amount of $4.29.
The answer is 4.665375. Rounded to the nearest cent is $4.67
Example Question #1 : How To Find The Amount Of Sales Tax
On a grocery shopping trip you spent $15 on meat, $5 on cheese, and $25 on produce. If the total bill was $48.15, what is the rate of sales tax on the food?
0.7%
0.75%
6.5%
7%
7.5%
7%
Tax = Total Bill - Cost of Food = 48.15 – (15 + 5 + 25) = $3.15
Percentage of Tax = Tax / Cost of Food = 3.15/ (15 + 5 + 25) = 3.15 / 45 = 0.07 = 7%
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