ACT Math › How to find proportion
The largest of three numbers is six less than four times the smallest number. The middle number is three more than twice the smallest number. The sum of twice the largest number, three more than three times the middle number, and four times the smallest number is 90. What is the value of the largest number?
14
10
12
18
22
Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.
2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5
4(6)-6 = 14
A group of 15 friends is having lunch together. Each person eats at least 2/3 of a pizza. What is the smallest number of whole pizzas needed for lunch?
10
5
15
7
The minimum number of whole pizzas needed is 15(2/3) = 10.
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?
600 feet
60 feet
167 feet
6 feet
1670 feet
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 = 50_x_ 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.
Max will be age X in 5 years. How old was he 4 years ago?
X +5
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
If there are 75 calories in a 6 oz glass of juice, how many calories will there be in an 8 oz glass?
We set up a proportion:
where
= calories.
We cross multiply to get , so there will be 100 calories in 8 oz of juice.
If a 12 oz can of lemonade has 75 calories; how many calories are in an 8 oz can of lemonade?
60
55
70
65
50
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
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)?
1.0
0.8
0.5
2.0
0.75
0.8 mile. Using some conversions: ( (24mi/1hr)*(1hr/60min)*2min = 0.8 mile
Tom, Tim, and Tammy ate an entire cake in the ratio of , respectively. If the cake had nine pieces, how many pieces did Tim eat?
For ratio problems, we want to sum the total numbers in the ratio to create a fraction. equal portions. Therefore, the fraction of the cake that Tim eats is simply
This, we need to multiply by the total number of pieces in the cake to find how many pieces he ate:
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.
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.
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?
30,000
12,230
363
10,000
25,500
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.