Solving a word problem using a system of linear equations of the form Ax + By = C

Question

A store is having a sale on walnuts and chocolate chips. For 2 pounds of walnuts and 5 pounds of chocolate chips, the total cost is $17. For 8 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $34. 

Find the cost for each pound of walnuts and each pound of chocolate chips.

Cost for each pound of chocolate chips:

Cost for each pound of walnuts:

Answer 1

Let x be the price of walnuts and y the price of chocolate chips.

2x + 5y = 17 (i)

8x + 3y = 34 (ii)

Multiply (i) by 4 to get

8x + 20y = 68

Subtract (ii) to get

17y = 34

Dividing by 17, we see that chocolate chips are $2.00 per pound.

Substituting y=2 in (i) or (ii), walnuts must be $3.50 per pound.