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

Answer 1

Let S = number of SHOES

Let K = number of pairs of SOCKS

First Equation: 2S + 3K = 86

Second Equation: 3S + 4K = 128

Multiply First Equation by 3:

6S + 9K = 258

Multiply Second Equation by -2:

-6S - 8K = - 256

Add the two new equations together:

K = 2 So, each pair of SOCKS cost $2

Plug 2 into the First Equation:

2S + (3)(2) = 86

2S + 6 = 86

2S = 80

S = 40. So, each pair of SHOES cost $40

ANSWER: THE COST OF A SINGLE PAIR OF SHOES AND SOCKS COST $42

CHECKING:

PLUG values of 40 and 2 into First Equation:

2S + 3K = (2)(40) + 3(2) = 80 + 6 = 86 Yes!

Hope this was helpful Jessica.