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.

Question

find the price of the hats and gloves

Answer 1

Alright, Jessie. Hopefully it's obvious to you what is causing the price difference, but we'll set this up the traditional way.

 

2g + 4h = 43

2g + 2h = 30

 

Now, hopefully by reading this, you can see that the two extra hats cost an extra $13, so one hat is $6.50.

 

2g + 2(6.5) = 30

2g + 13 = 30

2g = 17

g = 8.5

 

So one hat is $6.50 and one pair of gloves is $8.50.

 

To do the beginning algebraically, we see that both equations start with 2g. If we get both to have 2g by itself...

 

2g = 43 - 4h

2g = 30 - 2h

 

Well, if 2g equals two different things, they equal each other!

 

43 - 4h = 30 - 2h

2h = 13

h = 6.5

 

You would solve for g in the same manner as earlier.

 

If you still don't see that, we can multiply either equation by -1. Let's do the 2nd.

 

 2g + 4h = 43

-2g - 2h = -30

 

If we add the two equations, we get 2g = 13, so g = 6.5.

 

I hope this helps!