Question

A fruit salad consists of blueberries, raspberries, grapes, and cherries. There are equal numbers of raspberries and blueberries, three times as many grapes as cherries, and two times as many cherries as raspberries. Blueberries make up what percentage of the pieces of fruit in this fruit salad?

Answer 1

10%

Explanation:

blueberries, raspberries, grapes, and cherries

blueberries = raspberries

grapes = 3 × cherries

cherries = 2 × raspberries

grapes = 3 × 2 × raspberries

grapes = 6 × raspberries

cherries = 2 × raspberries

grapes = 6 × raspberries

blueberries = raspberries

Let blueberries = 1

Then

raspberries = 1

cherries = 2

grapes = 6

total = 1 + 1 + 2 + 6 = 10

blueberries = 1

percent of blueberries = 1/10 × 100% = 10%

Answer 2

10%

Explanation:

You want the percentage of pieces that are blueberries in a fruit salad with as many raspberries as blueberries, twice as many cherries as raspberries, and 3 times as many grapes as cherries.

Ratios

If we let B, R, G, C represent the numbers of blueberries, raspberries, grapes, and cherries, respectively, the ratios in the salad are ...

B : R = 1 : 1

C : G = 1 : 3

R : C = 1 : 2

In order to combine these ratios, we need to double the numbers in the C:G ratio to 2:6. Now we can write ...

B : R : C : G = 1 : 1 : 2 : 6

Blueberry fraction

Then the ratio of blueberries to the total is ...

1 : (1+1+2+6) = 1 : 10

The blueberries are 1/10 = 10% of the number of pieces of fruit.