Using elimination. I just need to check my answer!

Question

A merchant wants to mix pecans, which sell for $3.00 per pound, with cashews that sell for $6.00 per pound to make a 48 pound mixture he can export for $4 per pound. How many pounds of pecans and how many pounds of cashews should he use?

Answer 1

Let x = number of lb. of pecans

y = number of lb of cashews

 

x + y = 48            This represents the total amount of the mixture in lb.

 

3x + 6y = 48(4)    This represents the total cost of the mixture

 

3(x + y = 48)

3x + 6y = 192

 

We multiply the top equation by 3, and then subtract the two linear equations from each other to get:

 

3x + 3y = 144

3x + 6y = 192

 

-3y = -48

y = 16 lb of cashews

 

We know that x + y = 48

 

So x + 16 = 48

 

x = 32 lb of pecans