systems of equations

Question

The instructions say show 3 representations for each system of equations

 

1. Marcus wants to work for a shoe store in the mall Hoops athletic pays an employee $1,000 a month plus $5 for every pair of shoes he sells. Sports Inc pays an employee $500 a month and $10 for every pair of shoes he sells how many shoes would Marcus have to sell for both stores to pay him the same amount in a month? Which door should Marcus choose and why?

 

2. Brenda is moving to a new apartment. She can hire movers for $75 a day plus $0.45 a mile or she can move herself by renting a truck for 29.99 a day plus $0.85 per mile if it takes 2 days to move how many miles away can her new apartment be in order for both options to cost the same?

 

Can you please explain how to get the answers I am lost.

Answer 1

Hi Jackson.

 

I only live about 3 hours south of you!!!!  :-)

 

 

1.

To find out how much money Marcus will make at Hoops or Sports, need to know how much he will make even if he sells no shoes, then how much he will make on each pair of shoes.  When you add these together, you will know how much Marcus will make in one month at either store.  So....  here goes:

 

Hoops:  $1,000 + $5.00 (n)     n = the number of shoes Marcus sells

 

Sports:  $500 + $10.00 (n)

 

To find how how many shoes Marcus would have to sell to be paid the same, just set these equal to each other (in math, words like "same" usually translate to "=")

 

1000 + 5n = 500 + 10n

 

Solve for "n"

 

Subtract 500 from both sides

 

500 + 5n = 10n

 

Subtract 5n from both sides

 

500 = 5n

 

Divide both sides by 5

 

100 = n

 

So Marcus must sell 100 shoes at either store and he will make $1,500.

 

But if Marcus does not sell 100 shoes, let's say he only sells 80.

 

Hoops will pay him $1,000 + $5(80) = $1,400

Sports will pay him $500 + $10(80) = $1,300

 

So I would say that Marcus should work for Hoops because, in the event that he does not sell 100 or more pairs of shoes, he would make more money.

 

 

 

 

2.  (very similar to #1)

 

Movers cost $75(days)+ $0.45(miles)

Renting costs $29.99(days) + $0.85(miles)

 

We know that she needs 2 days, so replace each "days" with 2

 

Movers cost $75(2) + $0.45(miles)

Renting costs $29.99(2) + $0.85(miles)

 

For both options to cost the same, set these equal to each other.

 

150 + 0.45m = 59.98 + 0.85m            (m = miles)

 

Solve this.

 

Subtract 59.98 from both sides

 

90.02 + 0.45m = 0.85m

 

Subtract 0.45m  from both sides

 

90.02 = 0.40m

 

Divide both sides by 0.4

 

225.05 = m

 

So her new apartment can be 225.05 miles away and it will cost the same.