Question

Can you please help me solve and if you show work I would really appreciate it

Answer 1

You got the equations correct, great job on that!

Let "s" be the variable that represents how many shirts were bought. Let "p" represent the total price/cost.

Equation for the store at Town Center mall:

p = 80 + 3.5s (80 is base cost, and cost increases 3.5 per shirt)

Equation for the store in Arlington:

p = 120 + 2.5s (120 is base cost, and cost increases 2.5 per shirt)

We want to find a point where the systems are equal; thus, we are solving for a system of linear equations, and we already have the equations we need.

p = 80 + 3.5s

p = 120 + 2.5s

We know that variable "p" is equal for both equations; thus, we can combine both equations into:

80 + 3.5s = 120 + 2.5s

Subtract both sides by 2.5s

80 + 3.5s - 2.5s = 120 + 2.5s - 2.5s

80 + s = 120

Subtract both sides by 80

s = 40

Thus, both equations are equal when 40 shirts are bought.

To find the cost, use any of the two equations (or both) to find the total cost, which should be equal.

p = 80 + 3.5(40) = 220

p = 120 + 2.5(40) = 220

Thus, the total price/cost at both stores is $220.

Let me know if you need any clarifications, thanks!