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!
