At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tori bought two pairs of gloves and two hats for $30.00. What were the prices for the gloves and hats?

Let g = number of gloves and let h = number of hats. We’re going to write a system of equations.

2g+4h=43

2g+2h=30

Now I’m going to isolate a variable in one of the equations. Let’s isolate the g in the second equation

g+h=15

g=15-h

Next, I’m going to plug in my new equation for g into the first equation and solve for h.

2(15-h)+4h=43

30-2h+4h=43

30+2h=43

2h=13

h=6.5

Finally, I’m going to plug my solution for h into either equation (I’ll use the second one) and solve for g.

2g+2(6.5)=30

2g+13=30

2g=17

g=8.5

If I want to double check my answers, I can plug both values into the first equation and see if I get 43. The hats are $6.50 and the gloves are $8.50.

$6.50 and $8.50

_____________

RELATED: