Question 1208178
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Hi
Bob bought a pair of shoes. He also spent 1/4 of the remainder of his money on a pair of pants.  He had $189 left. If the cost of the pants was 3/7 the cost of the shoes, what is the price of the shoes.

Let the amount he started with, and cost of shoes, be A and S, respectively
After buying the shoes, he had A - S left
                           Amount spent on pants: {{{matrix(1,5, 1/4, of, A - S, "=", (A - S)/4)}}} 
        Amount remaining after purchase of pants: {{{matrix(1,5, 3/4, of, A - S, "=", 3(A - S)/4)}}}
Since $189 remained after purchase of pants, we get: {{{matrix(2,3, 3(A - S)/4, "=", 189, 3(A - S)/4, "=", 3(63)/1)}}}
                                                       {{{matrix(1,3, (A - S)/4, "=", 63)}}} ------ Canceling GCF, 3, in numerators                                                                            
Since cost of pants is {{{3/7}}} the cost of the shoes (S), so we get: {{{matrix(1,3, (A - S)/4, "=", 3S/7)}}}  
                                                                   {{{matrix(1,3, 63, "=", 3S/7)}}} ----- Substituting 63 for {{{(A - S)/4}}}
                                                                    3S = 7(63) --- Cross-multiplying
                                                  Cost of shoes, or {{{highlight_green(matrix(1,9, S, "=", 7(63)/3, "=", 7(21cross(63))/cross(3), "=", 7(21), "=", highlight("$147")))}}}</pre>