How many pounds of each is needed?

Question

john wants to mix walnuts(1.00 per pound)and cashews(3.00 per pound)to obtain a 10 pound mixture that will sell for 2.60 per pound. How many pounds of each is needed?

Answer 1

Let x be the number of pounds of walnuts

Let y be the number of pounds of cashews

 

Since you have 10 pounds of mixture, you can write x + y = 10.

 

The cost of walnuts is 1*x which is just x

The cost of cashews is 3y

 

Since the total cost is $2.60*10 which is $26, you can set up the second equation of x + 3y = 26.

 

So we've got the following system of equations:

x + y = 10

x + 3y = 26

 

This is already set up for the elimination method, so subtract the two equations to get,

-2y = -16    divide by -2

y = 8

 

Substitute back in to find x = 2.

 

So 2 pounds of walnuts and 8 pounds of cashews will give you the proper amount.