Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Harry 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, Harry sold 6 pairs of shoes and 9 pairs of boots, earning $198 in commission. Today, he sold 6 pairs of shoes and 6 pairs of boots, earning a total commission of $150. How much does Harry earn for the sale of each type of footwear?Harry earns $ for each pair of shoes and $ for each pair of boots.Submit
Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Harry 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, Harry sold 6 pairs of shoes and 9 pairs of boots, earning 150. How much does Harry earn for the sale of each type of footwear?Harry earns for each pair of boots.Submit
Solution
Let's denote the commission Harry earns for each pair of shoes as S and for each pair of boots as B.
From the problem, we can write the following system of equations:
- 6S + 9B = 198 (This represents the commission Harry earned yesterday)
- 6S + 6B = 150 (This represents the commission Harry earned today)
To solve this system using elimination, we can subtract the second equation from the first. This will eliminate S:
9B - 6B = 198 - 150 3B = 48
Divide both sides by 3 to solve for B:
B = 48 / 3 = $16
Substitute B = 16 into the second equation to solve for S:
6S + 6*16 = 150 6S + 96 = 150 6S = 150 - 96 6S = 54
Divide both sides by 6 to solve for S:
S = 54 / 6 = $9
So, Harry earns 16 for each pair of boots.
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