a student works part time in a shoe store. she earns a salary of $2,400 per week plus a commussion of $100 on each pair of boots and $50 on each pair of shoes s

Question

a student works part time in a shoe store. she earns a salary of $2,400 per week plus a commussion of $100 on each pair of boots and $50 on each pair of shoes she sells. during a certain week she made 30 sales and earned a total income of $5000. how many pairs of shoes did she sell?

Answer 1

Hi Alyssa.

 

First and foremost, a base weekly salary of $2,400 plus $50/$100 commissions? And it's part time?? Where do I sign up for this job??

 

But onto math stuff...

 

This is a system of equations problem in disguise. She has a base salary of $2,400 regardless of whether or not she's selling anything.

 

It says that she made $5,000 in total one week. $2,400 of this from her base salary, and the rest from sales. That means she made

 

$5,000 - $2,400 = $2,600

 

in sales commissions.

 

She can sell either boots or shoes. Let's call some variables.

 

B = number of pairs of boots student sells

S = number of pairs of shoes student sells

 

The problem states that she sold 30 pairs of boots/shoes. That means:

 

S + B = 30

 

We know that she makes $50 per pair of shoes sold and $100 per pair of boots sold, and she made a total of $2,600.

 

50*S + 100*B = 2600

 

So now we have 2 equations, 2 unknowns.

 

S + B = 30

50S + 100B = 2600

 

Divide the bottom equation by -50 and add the equations together.

 

S + B = 30

-S - 2B = -52

 

0 - B = -22

 

B = 22

 

S + 22 = 30

 

S = 8

 

She sold 8 pairs of shoes and 22 pairs of boots.

 

Always good to check your results.

 

Total number of shoes/boots should be 30.

 

8 + 22 = 30. Check.

 

Total amount of sales should be $2600

 

8*50 + 22*100 = 2600

 

400 + 2200 = 2600. Check.

 

Hope this helps.