If 2 pairs of shoes and 3 pairs of socks cost $86 and 3 pairs of the same shoes and 4 pairs of the same socks cost $128. How much does a single pair of shoez and socks cost?

Answer 1

This gives you simultaneous equations in two unknown variables, SHoes and SOcks (or x and y, if you prefer).

(1) 2SH + 3SO = 86

(2) 3SH + 4SO = 128

I will multiple (1) by 1.5 to get 3SH and hence eliminate one variable by subtracting (2) as follows...

3SH + 4.5SO = 129

-

3SH + 4SO = 128

=

0SH + 0.5SO = 1

=> SO = 2

now substitute SO value in (1) to get 2SH + 3(2) = 86

=> 2SH = 80

=> SH = 40

So socks are $2 a pair, and shoes are $40 a pair. And a single pair of shoes and socks costs $42.

Let's double-check by putting found values in the equations: so 2(40) + 3(2) = 86 as required. And 3(40) + 4(2) = 128 as required.