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.
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
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 !
A) Let's assume that x represents the total sales of athletic shoes in a month and y represents the monthly income.
Option 1: $500 per month plus a 4% commission on total sales
y = 500 + 0.04x
Option 2: $400 per month plus a 5% commission on total sales
y = 400 + 0.05x
B) To find the total price of athletic shoes that Kenisha needs to sell to earn the same income from each pay scale, we will set the two equations equal to each other and solve for x.
500 + 0.04x = 400 + 0.05x
Now, we solve for x:
0.04x - 0.05x = 400 - 500
-0.01x = -100
x = -100 / -0.01
x = 10,000
So, Kenisha needs to sell a total of $10,000 worth of athletic shoes to earn the same income from each pay scale.
C) To determine which offer is better, we can substitute the value of x back into the equations to find the corresponding y values.
For Option 1:
y = 500 + 0.04x
y = 500 + 0.04(10,000)
y = 500 + 400
y = 900
For Option 2:
y = 400 + 0.05x
y = 400 + 0.05(10,000)
y = 400 + 500
y = 900
Both options yield the same monthly income of $900.
Therefore, in this particular case, both offers result in the same income, so neither offer is better than the other.