Question 1206123
<br>
Let x be the number of apples he started with.<br>
After he threw away 1/4 of them, the number he had left was (3/4)x.<br>
After giving 15 to his freinds, the number he had left was (3/4)x-15.<br>
The number he had left was 2/3 of the number he started with, (2/3)x.<br>
{{{(3/4)x-15=(2/3)x}}}
{{{(3/4)x-(2/3)x=15}}}
{{{(1/12)x=15}}}
{{{x=15*12=180}}}<br>
He started with 180 apples; he finished with (2/3)*180 = 120 apples.<br>
Those 120 apples were packed into 14 boxes, some 6 per box and some 12 per box.<br>
Solving this second part of the problem formally....<br>
x boxes with 6 apples each, plus (14-x) boxes with 12 apples each, totals 120 apples:<br>
{{{6(x)+12(14-x)=120}}}
{{{6x+168-12x=120}}}
{{{-6x=-48}}}
{{{x=(-48)/-6=8}}}<br>
The number of boxes with 6 apples per box was x=8; the number of boxes with 12 apples each was 14-x = 6.<br>
ANSWERS:
(a) 120
(b) x=8<br>
Solving the second part of the problem mentally, using logical reasoning....<br>
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.<br>
And again the answer is 6 large boxes and 14-6 = 8 small boxes.<br>