Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. 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? Pedro earns $_____ for each pair of shoes and $_____ for each pair of boots.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  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?  Pedro earns $_____ for each pair of shoes and $_____ for each pair of boots.

Bytelearn · Accepted Answer

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 $.  Solve for $ s $: Subtract 96 from both sides to find $ s $. So, $ s = 9 $.

Full solution

More problems from Solve a system of equations using elimination: word problems

Related topics