Gwen

Gwen purchased 28 items, spending a total of $108. Balloons cost $3 each, bags of

candy cost $4 each, and caps cost $5 each. As students walked by, she gave each

student one of each. However, after 7 students, she found that she had run out of one

of the items, How many of each did Gwen purchase?

10, 11, and 7.

Step-by-step explanation:

28 items = $108

We know 7 of each item was handed out.

So we can start subtracting each item and its total cost.

First item:

7 balloons = $21

Then we have left:

21 items = $87

Next item:

7 candy = $28

Then we have left:

14 items = $59

Next item:

7 caps = $35

Then we have left:

7 items = $24

This is what we must solve. We know that one of the items ran out, so we just need to figure which two items still had more remaining.

There are only three ways you can split 7 into two different items. 1 and 6, 2 and 5, or 3 and 4. if you test each pair on the prices of the items you will see that only one possibility goes in evenly.

3 ($4.00 item) + 4 ($3.00) = $24

We can conclude that hats ran out at 7, balloons total was 11 (7+4), and candy total was 10 (7+3).