SOLUTION: Leon bought some apples. He gave 15 of the apples to his friends and threw away 1/4 of them. He was left with 2/3 of the apples. He then packed the remaining apples into 14 boxes.

Question 1206123: Leon bought some apples. He gave 15 of the apples to his friends and threw away 1/4 of them. He was left with 2/3 of the apples. He then packed the remaining apples into 14 boxes. Some boxes contained 6 apples while the rest contained 12.
(a) How many apples were packed into the 14 boxes?
(b) How many boxes contained 6 apples?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let x be the number of apples he started with.

After he threw away 1/4 of them, the number he had left was (3/4)x.

After giving 15 to his freinds, the number he had left was (3/4)x-15.

The number he had left was 2/3 of the number he started with, (2/3)x.

He started with 180 apples; he finished with (2/3)*180 = 120 apples.

Those 120 apples were packed into 14 boxes, some 6 per box and some 12 per box.

Solving this second part of the problem formally....

x boxes with 6 apples each, plus (14-x) boxes with 12 apples each, totals 120 apples:

The number of boxes with 6 apples per box was x=8; the number of boxes with 12 apples each was 14-x = 6.

ANSWERS:
(a) 120
(b) x=8

Solving the second part of the problem mentally, using logical reasoning....

If all 14 boxes contained 6 apples each, the boxes would contain a total of 14*6 = 84 apples.
But the number of apples in the boxes was 120, which is 120-84 = 36 more.
Each large box contains 6 more apples than each small box; so the number of large boxes needed for those additional 36 apples is 36/6 = 6.

And again the answer is 6 large boxes and 14-6 = 8 small boxes.

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