Nolan is a shoe salesman, and he works on commission. This week, there is a special incentive to sell shoes and boots by a certain company. Yesterday, Nolan sold 3 pairs of shoes and 5 pairs of boots, earning $127 in commission. Today, he sold 5 pairs of shoes and 8 pairs of boots, earning a total commission of $205. How much does Nolan earn for the sale of a pair of shoes and how much does Nolan earn for the sale of a pair of boots.
Let's assume the commission for a pair of shoes is $s, and the commission for a pair of boots is $b.
Yesterday, Nolan sold 3 pairs of shoes and 5 pairs of boots, earning a total commission of 3s + 5b = $127. ----(1)
Today, he sold 5 pairs of shoes and 8 pairs of boots, earning a total commission of 5s + 8b = $205. ----(2)
Let's solve these two equations simultaneously to find the values of s and b.
Multiplying equation (1) by 5 and equation (2) by 3, we have:
15s + 25b = 635 ----(3)
15s + 24b = 615 ----(4)
Subtracting equation (4) from equation (3), we get:
15s + 25b - (15s + 24b) = 635 - 615
15s + 25b - 15s - 24b = 20
b = 20
Substituting the obtained value of b into equation (3), we have:
15s + 25(20) = 635
15s + 500 = 635
15s = 635 - 500
15s = 135
s = 135 / 15
s = <<9=9>>9
Therefore, Nolan earns $9 for the sale of a pair of shoes and $20 for the sale of a pair of boots.