Question

A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commission for for selling 3 suits and a pair of shoes. The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes. How much commission for selling each suit and each pairs of shoes? Solve by substitution.

Answer 1

The commission for selling each suit is $ 13 and commission for selling each pairs of shoes is $ 8

Solution:

Let "a" be the commission earned on each suit

Let "b" be the commission earned on each pair of soes

One week, she earned $47 in commission for for selling 3 suits and a pair of shoes

Therefore, we frame a equation as:

`3 * a + 1 * b = 47\\\\3a + b = 47\\\\Isolate\ for\ b\\\\b = 47 - 3a --------- eqn 1`

The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes

Therefore, we frame a equation as:

`7 * a + 2 * b = 107\\\\7a + 2b = 107 ---------- eqn 2`

Substitute eqn 1 in eqn 2

7a + 2(47 - 3a) = 107

7a + 94 - 6a = 107

a = 107 - 94

a = 13

Substitute a = 13 in eqn 1

b = 47 - 3(13)

b = 47 - 39

b = 8

Thus commission for selling each suit is $ 13 and commission for selling each pairs of shoes is $ 8