I am not understanding how to solve this. CAN ANYONE HELP ME PLEASE?

Question

A store has in its inventory sweaters and turtlenecks with a combined value of $3585. a sweater cost $45 while a turtleneck cost $32.There are 54 less turtle necks than sweaters. How many of each type of garment are in the store?

I have the answer, but am not understanding how it is accomplished.

ANS: 69 sweaters and 15 turtlenecks

Answer 1

You are looking for 2 unknowns: the number of sweaters and the number of turtlenecks. So let S = the number of sweaters and T = the number of turtlenecks.

"There are 54 less turtlenecks than sweaters" ==> T = S - 54

The value of S sweaters is 45S, and the value of T turtlenecks is 32T, so the combined value is

45S + 32T = 3585

Substitute (S - 54) for T in the 2nd equation to get

45S + 32(S - 54) = 3585

45S + 32S - 1728 = 3585

77S = 5313

S = 69

Then T = S - 54 = 69 - 54 = 15