Question

Madison and Madelyn work at a furniture store. Madison is paid $255 per week plus 2.5% of her total sales in dollars, x, which can be represented by g(x) = 255 + 0.025x. Madelyn is paid $131 per week plus 6.5% of her total sales in dollars, x, which can be represented by f(x) = 131 + 0.065x. Determine the value of x, in dollars, that will make their weekly pay the same.

A. $1,850
B. $3,100
C. $2,500
D. $2,250

Answer 1

By setting the pay equations for Madison and Madelyn equal and solving for x, the weekly sales needed to equalize their pay is found to be $3,100.

Step-by-step explanation:

To find the value of x, in dollars, that will make Madison and Madelyn's weekly pay the same, we set their pay equations equal to each other:

Madison: g(x) = 255 + 0.025x
Madelyn: f(x) = 131 + 0.065x

Equality of pay:
255 + 0.025x = 131 + 0.065x

Now we solve for x by first getting the x-terms on one side of the equation:
0.025x - 0.065x = 131 - 255

This simplifies to:
-0.04x = -124

Divide both sides by -0.04 to isolate x:

x = -124 / -0.04

x = $3,100

Therefore, both Madison and Madelyn will earn the same amount when their total sales in dollars, x, is $3,100.