Question

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

Answer 1

1/5 were granola
1/2 of the remaining. The remaining is 4/5.
So 1/2 of 4/5 = (1/2)(4/5) = 4/10 = 2/5
So 1/5 is granola, and 2/5 were containers of popcorn leaving 2/5 to be divided 3 equal ways among apples, rice cakes, and yogurt.
So if there was 8 apples, 8 rice cakes, and 8 yogurts that make up 2/5 of this....so 2/5 is 24
so...(2/5) / 24 = (5/5) / x --- 2/5 to 24 = 5/5 to x)
cross multiply
2/5x = 24(5/5)
2/5x = 24
x = 24/(2/5)
x = 24 * 5/2
x = 120/2
x = 60

check...
total 60
1/5 granola : 1/5(60) = 60/5 = 12
2/5 popcorn : 2/5(60) = 120/5 = 24
2/5 (8 apples, 8 rice cakes, 8 yogurts) = 24
---------------------------------------add
5/5 = 24 + 24 + 12 = 60

He originally had 60 items