Fraction of ice cream sold?

Question

At an ice cream parlour, chocolate, vanilla and strawberry ice cream were at an ratio of 5:7:8

After 20% of chocolate, 1/3 of vanilla and some strawberry ice cream were sold.

The amount of strawberry ice cream left was 3/7 of the total amount of ice cream are left

What fraction of the strawberry ice cream were sold?

Answer 1

The ratio 5:7:8 can be rewitten as 0.25, 0.35 and 0.40, the proportions of total ice cream that is chocolate, vanilla and strawberry.

Note 0.25 = 5/20, 0.35 = 7/20 and 0.40 = 8/20, and the denominator 20 = 5+7+8.

If 20% of the chocolate is sold, then 0.25 - 0.05 (20% of 0.25) = 0.20 of chocolate remains.

If 1/3 or 0.33333... of the vanilla is sold, then 0.35 - 0.11666... = 0.23333... of vanilla remains.

Before any strawberry was sold, the remaining ice cream as a proportion (rounded to 2 decimal places) of the original total is 0.20+0.23+0.40 = 0.83

The amount of strawberry ice cream left after sale was 3/7 of 0.83 = 0.428571428 * 0.833333333 = 0.357142857 ~ 0.36.

Therefore 0.40 - 0.36 = 0.04 = 4% of the available strawberry ice cream was sold.