At intermission, Xavier sold refreshments. Of the items he had, 1/5 were granola bars and 1/2 of the remaining items were containers of popcorn. The rest were divided equally among apples, rice cake, and containers of yogurt. Xavier sold the 8 apples he had. How many items did he originally have?

Answer 1

x = number of items

He have:

x / 5 of granola and x / 2 popcorn

x / 5 + x / 2 = 2 x / 10 + 5 x / 10 = 7 x / 10

He had 7 x / 10 granola and popcorn.

The rest = 10 x / 10 - 7 x / 10 = 3 x / 10

The rest were divided equally among apples, rice cake, and containers of yogurt mean:

The rest is divided into 3 equal parts each:

( 3 x / 10 ) / 3 = 3 x / 30 = x / 10

So 8 apples = x / 10

x / 10 = 8

Multiply both sides by 10

x = 80

He originally have 80 items.

Proof:

He had 7 x / 10 granola and popcorn.

He had 7 ∙ 80 / 10 = 560 / 10 = 56 granola and popcorn.

The rest = 80 - 56 = 24

The rest were divided equally among apples, rice cake, and containers of yogurt.

The rest / 3 = 24 / 3 = 8

He have 8 among apples, 8 rice cake, 8 containers of yogurt.