Michelle P. answered • 04/11/21

A pre-student teacher with a passion for math!

Hi Mandi,

We can set up a system of equations to determine the price of each shirt. Let *s* be the number of shirts and *h* be the number of hats.

We know that Eva paid $154 for 2 shirts and 5 hats. In equation form, this looks like

2*s*+5*h*=154

We also know that Eva could get 3 shirts and 4 hats for $168. In equation form, this looks like

3*s*+4*h*=168

There's a couple of ways we can go from here. You can use the elimination method or the substitution method to solve for each variable. I'm going to use the substitution method.

We need to take one of the equations and isolate one of the variables. I'll isolate *s* in the first equation. First, subtract 5*h* from both sides.

2*s* = 154 - 5*h*

Divide both sides by 2 and you should get

*s* = 77 - (5/2)*h*

We can substitute this *s* equation into our second equation to figure out what *h* is. This looks like

3*s*+4*h *= 168

3(77-(5/2)*h*) +4*h* = 168

Distribute the 3 and combine like terms to get

231 - (15/2)*h* +4*h = *168

231 - (7/2)*h* = 168

-(7/2)*h* = -63

* h* = 18

**So each hat costs $18**. Finally, we plug *h* into our *s* equation. This looks like

* s* = 77 - (5/2)*h*

* s* = 77 - (5/2)(18)

* s* = 32

**And we find that each shirt costs $32.**

Hope this helps!