Asked by Johnny
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?
Answers
Answered by
Bosnian
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.
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.
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