Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Pedro 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, Pedro sold $1$ pair of shoes and $6$ pairs of boots, earning $\$105$ in commission. Today, he sold $2$ pairs of shoes and $8$ pairs of boots, earning a total commission of $\$146$ . How much does Pedro earn for the sale of each type of footwear? $\newline$ Pedro earns $\$$ _ for each pair of shoes and $\$$ _ for each pair of boots.

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Grade 8

Solve a system of equations using elimination: word problems

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Pedro 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, Pedro sold

1

pair of shoes and

6

pairs of boots, earning

\$105

in commission. Today, he sold

2

pairs of shoes and

8

pairs of boots, earning a total commission of

\$146

. How much does Pedro earn for the sale of each type of footwear?

\newline

Pedro earns

\$

_____ for each pair of shoes and

\$

_____ for each pair of boots.

Define Variables: Let's define the variables: Let $s$ be the commission for a pair of shoes and $b$ be the commission for a pair of boots.
Write Equations: Write the equations based on the given information: From yesterday's sales, we have the equation $s + 6b = 105$ . From today's sales, we have $2s + 8b = 146$ .
Use Elimination: Use elimination to solve the system: Multiply the first equation by $2$ to align the coefficients of $s$ for elimination. So, $2s + 12b = 210$ .
Subtract Equations: Subtract the first modified equation from the second equation: $(2s + 8b) - (2s + 12b) = 146 - 210$ . Simplify to get $-4b = -64$ .
Solve for b: Solve for $b$ : Divide both sides by $-4$ to find $b$ . So, $b = 16$ .
Substitute and Solve for s: Substitute $b = 16$ back into the first equation to find $s$ : $s + 6(16) = 105$ . Simplify to get $s + 96 = 105$ .
Substitute and Solve for s: Substitute $b = 16$ back into the first equation to find $s$ : $s + 6(16) = 105$ . Simplify to get $s + 96 = 105$ . Solve for $s$ : Subtract $96$ from both sides to find $s$ . So, $s = 9$ .