word problem

Question

A store is having a sale on walnuts and chocolate chips. For 5
pounds of walnuts and 2
pounds of chocolate chips, the total cost is
13 . For 3
pounds of walnuts and 8
pounds of chocolate chips, the total cost is
18. Find the cost for each pound of walnuts and each pound of chocolate chips.

Answer 1

Edith, we are going to make a system of equations.

 

5w + 2c = 13

3w + 8c = 18

 

Our best bet to solve this is elimination. Right now, nothing eliminates. 5w + 3w = 8w and 2c + 8c = 10c. We need opposite coefficients in either variable.

 

Hmmm, what if we multiply the top by -4?

 

-4(5w + 2c) = -4(13)

-20w - 8c = -52

 

Now we have opposites with the p

 

-20w - 8c = -52

3w + 8c = 18

 

-17w = -34

w = 2

 

3(2) + 8c = 18

6 + 8c = 18

8c = 12

c = 1.5

 

Walnuts are $2/lb and chocolate chips are $1.50/lb.