SOLUTION: 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

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: 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      Log On


   

Question 1162077: 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?
Found 3 solutions by ankor@dixie-net.com, MathTherapy, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Let x = no. of items he had originally
:
Of the items he had, 1/5 were granola bars and 1/2 of the remaining items were containers of popcorn.
half of the remaining items 4%2F5x * 1%2F2 = 2%2F5x were popcorn
:
The rest were divided equally among apples, rice cake, and containers of yogurt.
Xavier sold the 8 apples he had.
This means the rest were a total of 3(8) = 24 items
:
How many items did he originally have
:
x = bars + popcorn + the rest
x = 1%2F5x + 2%2F5x + 24
x = 3%2F5 + 24
x - 3%2F5x = 24
2%2F5x = 24
multiply both sides by 5
3x = 120
x = 120/3
x = 40 items total


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

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?
Correct answer: highlight_green%28matrix%281%2C5%2C+Original%2C+number%2C+of%2C+%22items%3A%22%2C+60%29%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

1%2F5  of all items were granola;  the rest is  4%2F5  of the items.


Half  of this  4%2F5  items were containers of popcorn.


The other half, or the rest, is  2%2F5  of the items.


These  2%2F5  are divided equally in 3 categories: apples, rice cakes, and containers of yogurt.


Hence, each of the three categories is  2%2F%283%2A5%29 = 2%2F15  of the items.


Since 2%2F15  (apples)  is  8 item,  hence  1%2F15 is 4 items.


It means that the total number of items was  15*4 = 60.



ANSWER.  He originally had 60 items.


Solved.


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This problem is for  3rd - 4th - 5th  grade level,  when young students learn fractions and learn
manipulating fractions,  but don't know equations yet.