Question 1170779
<br>
A setup using formal algebra....<br>
f = # of fruit pies
m = # of meat pies<br>
The total sales, at $7 for each fruit pie and $10 for each meat pie, was $424:<br>
(1) {{{7f+10m = 424}}}<br>
The total number of pies was 52:<br>
(2) {{{f+m=52}}}<br>
One possible way to solve this pair of equation is to multiply the second equation by 10 and compare the resulting equation to (1):<br>
{{{10f+10m = 520}}}
{{{7f+10m = 424}}}
{{{3f = 96}}}  (the difference between those two equations)
{{{f = 32}}}<br>
ANSWER: the number of fruit pies sold was 32; the number of meat pies was 52-32=20.<br>
You can solve the problem informally, using EXACTLY the same calculations, like this:<br>
(1) If all 52 pies were meat pies, the total sales would be $520.
(2) The actual total sales was $424, which is $96 less than $520.
(3) Each fruit pie costs $3 less than each meat pie.
(4) The number of fruit pies sold, to bring the sales total down $96, from $520 to $424, is $96/$3 = 32.<br>