QR6: Apply ratios to solve problems

A ratio of apples to oranges is 2:3. If there are 6 apples, how many oranges are there?

• 6

• 8

• 9

• 12

Answer explanation

The ratio of apples to oranges is 2:3. With 6 apples, we set up the proportion: 2/3 = 6/x. Cross-multiplying gives 2x = 18, so x = 9. Therefore, there are 9 oranges.

A ratio is 1:4. If the first value is 5, what is the second value?

• 10

• 15

• 20

• 25

Answer explanation

The ratio 1:4 means for every 1 unit of the first value, there are 4 units of the second value. If the first value is 5, the second value is 5 * 4 = 20. Thus, the correct answer is 20.

A ratio of cats to dogs is 3:2. If there are 12 cats, how many dogs are there?

• 6

• 8

• 10

• 18

Answer explanation

The ratio of cats to dogs is 3:2. With 12 cats, we set up the proportion: 3/2 = 12/x. Cross-multiplying gives 3x = 24, so x = 8. Therefore, there are 8 dogs.

Tags

CCSS.7.RP.A.3

A recipe calls for a ratio of 3 cups flour to 2 cups sugar. How much sugar is needed for 12 cups of flour?

• 6

• 8

• 10

• 12

Answer explanation

The ratio of flour to sugar is 3:2. For 12 cups of flour, set up the proportion: (2 cups sugar / 3 cups flour) = (x cups sugar / 12 cups flour). Solving gives x = 8 cups of sugar.

A map scale is 1 inch : 8 miles. How many miles does 7 inches represent?

• 40

• 48

• 56

• 64

Answer explanation

The map scale indicates 1 inch represents 8 miles. Therefore, 7 inches equals 7 x 8 = 56 miles. Thus, the correct answer is 56.

Tags

CCSS.6.RP.A.3B

A classroom ratio is 5 boys to 7 girls. If there are 35 girls, how many boys are there?

• 20

• 25

• 30

• 35

Answer explanation

The ratio of boys to girls is 5:7. With 35 girls, we set up the proportion 5/7 = x/35. Solving for x gives x = (5 * 35) / 7 = 25. Thus, there are 25 boys.

A mixture uses a ratio of 4 parts water to 1 part syrup. If there are 20 cups of water, how much syrup is needed?

• 4

• 5

• 6

• 8

Answer explanation

The ratio of water to syrup is 4:1. With 20 cups of water, divide by 4 to find the parts: 20 ÷ 4 = 5. Therefore, 5 cups of syrup are needed.

A car travels 180 miles using 6 gallons of gas. At the same rate, how many miles will it travel using 10 gallons?

• 240

• 270

• 300

• 360

Answer explanation

The car's rate is 180 miles per 6 gallons, or 30 miles per gallon. For 10 gallons, it will travel 30 x 10 = 300 miles. Thus, the correct answer is 300.

Tags

CCSS.6.RP.A.3B

A store sells 3 shirts for $45. At the same rate, how much do 5 shirts cost?

• $60

• $65

• $70

• $75

Answer explanation

The cost per shirt is $45 / 3 = $15. For 5 shirts, the cost is 5 * $15 = $75. Therefore, the correct answer is $75.

Tags

CCSS.6.RP.A.3B

A recipe uses a ratio of 2:5 (sugar to flour). If you have 25 cups of flour, how much sugar do you need?

• 5

• 8

• 10

• 12

Answer explanation

The ratio of sugar to flour is 2:5. If you have 25 cups of flour, set up the proportion: 2/5 = x/25. Solving for x gives x = (2/5) * 25 = 10. Therefore, you need 10 cups of sugar.