Question 1186434

Derek’s shop sells shirts and pants. A pair of pants is sold at $48 and a shirt is sold
at 3/4 the price of a pair of pants.   On Friday, Derek sold 2/3 of the clothing in his shop
and collected $3672.  2/5 of the clothing sold were pants.

(a)  How many shirts did Derek sell on Friday?
(b)  How many clothing were left unsold in the shop after Friday?
<pre>One of the other person's answers is WRONG! The number of shirts sold was NOT 36. 

As {{{2/3}}} of clothing was sold, number of clothing sold = 2x, and number of unsold clothing = x

As {{{2/5}}} of clothing sold were pants, number of pants sold = {{{matrix(1,3, (2/5)2x, "=", 4x/5)}}}
If {{{2/5}}} of clothing sold were pants, then {{{3/5}}} of clothing sold, or {{{matrix(1,3, (3/5)2x, "=", 6x/5)}}}, were shirts

A pair of pants costs $48, and as a shirt cost ¾ a pants’ price, a shirt costs: ¾ * 48 = 36

Since {{{4x/5}}} pants, and {{{6x/5}}} shirts sold for $3,672, we get:
{{{matrix(1,3, 48(4x/5) + 36(6x/5), "=", "3,672")}}}
  {{{matrix(1,3, 4(4x/5) + 3(6x/5), "=", 306)}}} ------- Dividing by GCF, 12
        {{{matrix(1,3, 16x/5 + 18x/5, "=", 306)}}}  
        16x + 18x = 5(306) ----- Multiplying by LCD, 5
              34x = 5(306)
Number of unsold pieces of clothing, or {{{highlight_green(matrix(1,7, x, "=", 5(306)/34, "=", 5(9), "=", 45))}}}

Number of shirts sold: {{{highlight_green(matrix(1,7, 6x/5, "=", 6(45)/5, "=", 6(9), "=", 54))}}}</pre>