Kenisha sells athletic shoes part-time at a department store. She can either earn $500 per month plus a 4% commission on her total sales or $400 per month plus a 5% commission on total sales.

Question

A)write a system of equations to represent the situation.
B)what is the total price of the athletic shoes kenisha needs to sell to earn te same income from each pay scale.
C)which is the better offer

and we're doing substitution so i need to know 2 equations with x and y variables in both

Answer 1

Hello

the 2 variables that u have to conider are the total sales that we will call x in our case, and Kenisha's income that we will call y

A) if we translate the first sentence to an equation, we understand that she earns a fixed amount + a percentage on the total sales, thus we get the following system:

y = 500 + 4*x/100 (1)
y = 400 + 5*x/100 (2)

(we divide by a hundred because it's a perCENTage)

B) earning the same income means the value of the variable y is the same for both equations. Therefore, we can write : y = y and get the following :

500 + 4*x/100 = 400 + 5*x/100

that gives us a value of x = 10 000

C) so if you think a little bit, she has to sell for 10 000 $ of shoes in order for both to be equal ! Since it's very risky and even impossible, let's pretend she did half of it and only sold for 5 000 $

We then replace the x by 5 000 and see which y value is the highest (means which income is the highest)

by replacing x by 5 000 u find that for the first equation , y = 700 $ and for the second y = 650 $

so the first solution (500$ + 4% of the sales) is the best solution since it provides a safer and higher income.

PS : i don't think the last question is very appropriate for 8th grade students but anyway here you go !