All ACT Math Resources
Example Question #1 : How To Find Proportion
A Hospital building that is 20 feet tall casts a shadow of 10 feet. There is a Financial building nearby that is 60 feet tall. How tall is the shadow cast by the Financial building?
To solve this question, you must set up a ratio between the height of the building and the shadow it casts. The ratio should be: 20/10 = 60/x. When you solve for x, you should get 30 ft. 10 is incorrect because if the financial building is taller, its shadow has to be larger. Options 60 and 120 are incorrect because is incorrect because the shadow of the building cannot be equal to or larger than the height of the building.
Example Question #2 : How To Find Proportion
Max will be age X in 5 years. How old was he 4 years ago?
X – 9
X – 5
X – 4
X – 9
Max will be X in 5 years. So today he is X -5 and 4 years ago he was (X-5) - 4, that is X – 9. It always helps to put numbers into the equations. Example: Max will be 12 in 5 years. How old was he 4 years ago? So today Max is 12 – 5 = 7. Therefore, four years ago he was 7 -4 =3. Which is 12-5-4 =12-9 = 3
Example Question #43 : Proportion / Ratio / Rate
If a pizza pie that has 16 slices and costs $12.00 is to be shared among 8 friends, how much should each person contribute?
It is $12 divided by 8 which is $1.50. The number of slices in the pizza pie is not relevant in this question.
Example Question #1481 : Act Math
In a school relay race, every 5-man team must sprint 110 yards total. However, Jim’s team is short a person. Thus, Jim must run two sections for his team. How far does Jim have to run?
We first find out how much each person must run. Thus we take 110/5 to get 22 yards. However, Jim must run twice the amount of a normal competitor, so we multiply by 2 to get 44 yards.
Example Question #46 : Proportion / Ratio / Rate
A building that is 30 feet tall casts a shadow that is 50 feet long. If another building casts a shadow that is 100 feet long, how tall is the building?
This problem can be set up as a proportion: 30 feet/x feet = 50 feet/100 feet. To solve, we simply cross multiply: (30 feet * 100 feet) = (50 feet * x feet). Thus, 3000 feet = 50x feet. To solve for x, divide each side by 50. Therefore, x = 60 feet. If you got 167 feet, you may have set up the proportion incorrectly by mixing up the height of the building with the length of the shadow. If you got 6 feet or 600 feet, you may have made a computational error. If you got 1670 feet, you may have set the proportion up incorrectly and made a computational error.
Example Question #4 : How To Find Proportion
If a bicyclist can bike 24 miles per hour, how far (in miles) can he travel in 2 minutes, assuming he bikes at a constant speed (answer rounded to the nearest tenth)?
0.8 mile. Using some conversions: ( (24mi/1hr)*(1hr/60min)*2min = 0.8 mile
Example Question #5 : How To Find Proportion
If 10,000 lbs of cement makes 85,000 lbs of concrete, how many pounds of concrete can be made with 3,000 pounds of cement?
25,500 lbs of concrete. Setting up a ratio with x representing the number of pounds concrete the 3,000 of cement produces, we obtain the relation: (10,000/85,000) = (3,000/x), x = 25,500 pounds of concrete.
Example Question #1482 : Act Math
There are 150 students in a lecture hall class in college. 12% of the students received an A. 20 students received a B. Twice the number of students who earned an A received a C. The remainder of the students received a D. Which grade did the students receive more than any other?
The students who got D's.
The students who got C's
The students who got B's
The students who got A's.
Cannot be determined.
The students who got D's.
First find 12% of 150, so 0.12 * 150 = 18 students received an A.
20 students received a B, and 36 students received a C (double the A's).
To find the number of D-grades, all we have to do is subtract these from the total (since there were no grades of F),
Thus: 150 – 18 – 20 – 36 = 76 students who received a D in the course, which is the most common grade.
Example Question #7 : How To Find Proportion
A brownie recipes calls for a 1:5 ratio of water to brownie mix. If you need 90 cups of brownie mix, how much water do you need?
First set up a proportion, 1/5 = x/90, then solve for x: 5x = 90 → x = 18 cups.
Example Question #414 : Arithmetic
If a 12 oz can of lemonade has 75 calories; how many calories are in an 8 oz can of lemonade?
A proportion is a statement of equality between two fractions or two ratios. Set up a proportion between the size of the drink and the calories. To solve a proportion cross multiply and solve the resulting equation.
75/12 = x/8 → 150/24 = 3x/24 → 50/8 = x/8 → x = 50