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

Question

A store is having a sale on almonds and jelly beans. For 3 pounds of almonds and 5 pounds of jellybeans, the total cost is $25. For 9 pounds of almonds and 7 pounds of jellybeans, the total cost is $53. Find the cost for each pound of elements in each pound of jellybeans.

Answer 1

3a +5j = 25

multiply by 3

9a +15j = 75

subtract

9a + 7j = 53

8j = 22

j=22/8= $2.75 per jellybean pound

a = (25-13.75)/3= 11.25/3=$3.75 per almond pound