writing systems of equations and word problems

Question

An art teacher bought some large canvases at $7 each and some small ones at $4 each paying $219 in total altogether he bought 39 campuses how many large canvases did he buy?

 

Can you please explain how to set up the equation so I can solve the problem

 

Answer 1

Let x be the number of large canvases and y the number of small canvases.

 

You get two equations in x and y:

 

x + y = 39

7x + 4y = 219

 

The problem is to solve for x, so you can start by eliminating y:

 

y = 39 - x

 

7x + 4(39 - x) = 219

 

7x + 156 - 4x = 219

 

3x = 63

 

x = 21.

 

The art teacher bought 21 large canvases.

Answer 2

These problems are some of my personal favorites.

 

x = number of large canvasses

y = number of small

 

Equation for the number of canvasses purchased:

 

x + y = 39

 

Equation for the cash spent:

 

7x + 4y = 219

It's set up. You should be good to go. Cheers!