Proportions
Solve for x:
7 / x = 14 / 28
x = 14
If there are 12 boys and 8 girls in a class, what is the ratio of boys to girls in simplest form?
3:2
If the two angles are complementary and one angle is 4 times the other, what is the ratio of the larger angle to the smaller?
4x + x = 90
x = 18
ANSWER: 72:18
The ratio of two supplementary angles is 7:2. Find the measures of BOTH angles.
7x + 2x = 180, x = 20
140 degrees and 40 degrees
Solve for x:
10 / (2x - 9) = 20 / 9
20 (2x-9) = 10 (9)
x = 6.75
A fruit basket contains 12 apples, 18 bananas, and 30 oranges. What is the ratio of apples to the total number of fruits in simplest form?
12:60 but simplified is 1:5
If two angles are in the ratio 2:3 and they are supplementary, what are their measures?
2x + 3x = 180 --> x = 36
Answer: 72 degrees and 108 degrees
A recipe requires a ratio of milk to water of 5:2. If you use 10 cups of milk, how many cups of water do you need? (You must show work)
5 / 2 = 10 / x
x = 4
Answer: 4 cups of water
If 5 pounds of apples cost $3, how much would 8 pounds cost? (Set up a proportion)
3 / 5 = x / 8 --> x = 4.80
Answer: $4.80
If the ratio of cats to dogs is 4:5 and there are 20 cats, how many dogs are there?
4x = 20 --> x = 5
5 (5 ) = 25 dogs
The ratio of the measures of the sides of a triangle is 4:9:3. If the perimeter is 304 meters, find the length of the shortest side.
4x + 9x + 3x = 304
16x = 304 --> x = 19
Shortest Side (3x) --> 57 meters
In a class of 40 students, the ratio of boys to girls is 3:5. If 6 more boys join the class, what will be the new ratio of boys to girls?
3x + 5x = 40 --> x = 5
15 boys to 25 girls --> add 6 boys
ANSWER: 21: 25
Solve for x:
(4x + 2) / 3 = (5x -1 ) / 4
4 (4x + 2) = 3 (5x - 1)
x = -11
In a survey of 100 people, the ratio of people who prefer Dr. Pepper to those who prefer Diet Coke is 7:3. If 20 more people who prefer Diet Coke are added to the survey, what is the new ratio of Dr. Pepper drinkers to Diet Coke drinkers?
7x + 3x = 100, 10x = 100, x = 10
--> 70 DP and 30 DC but add 20 DC
70:50 which simplifies to 7:5
The ratio of the measures of the sides of a triangle is 2:8:9. If the perimeter of the triangle is 76 inches, find the length of each side.
2x + 8x + 9x = 76
x = 4
Answer: 8 inches, 32 inches, 36 inches
Solve for x:
6 / (x + 16) = 7 / (3x+ 3 )
6 (3x + 3) = 7 (x + 16)
11x = 94
x = 8.5
A car travels 180 miles in 3 hours. If it travels at the same speed, how far will it go in 5 hours? (Set up and solve a proportion)
180 / 3 = x / 5
x = 300
Answer: 300 miles
In a fruit basket, there are 6 apples, 4 bananas, and 10 oranges. What is the ratio of apples to the total number of fruits? (Simplified ratio)
6:20 BUT simplified = 3:10
The angles of a triangle are in the ratio 3:4:5. What are the measures of the angles?
3x + 4x + 5x = 180 --> 12x = 180 so x = 15
ANS: 45 degrees, 60 degrees, and 75 degrees
In a triangle, the lengths of the sides are in the ratio 5:12:13. If the perimeter of the triangle is 60 cm, what are the lengths of each side?
5x + 12x + 13x = 60
x = 2
Lengths are 10 cm, 24 cm, and 26 cm.