Question

A store is having a sale on jelly beans and almonds. For 7 pounds of jelly beans and 9 pounds of almonds, the total cost is $46. For 5 pounds of jelly beans and 3 pounds of almonds, the total cost is $20. Find the cost for each pound of jelly beans and each pound of almonds.​

Answer 1

• jelly beans: $1.75 per pound
• almonds: $3.75 per pound

Explanation:

You want to know the prices of jelly beans and almonds when you can buy 7 pounds of jelly beans and 9 pounds of almonds for $46, or 5 pounds of jelly beans and 3 pounds of almonds for $20.

Equations

The equations describing each purchase can be written as ...

• 7j +9a = 46
• 5j +3a = 20

Solution

A graphing calculator plots these equations easily, and shows you the solution is (j, a) = (1.75, 3.75).

Jelly beans are $1.75 per pound; almonds are $3.75 per pound.

Elimination

If you like, you can solve these equations by elimination. We notice the coefficients of 'a' have a simple ratio, so we can eliminate 'a' easily.

3(5j +3a) -(7j +9a) = 3(20) -(46) . . . . . subtract the first from 3 times the second

8j = 14 . . . . . simplify

j = 1.75 . . . . . divide by 8

Substituting into the second equation, we get ...

5(1.75) +3a = 20

3a = 11.25 . . . . . . . . . subtract 8.75

a = 3.75 . . . . . . . . divide by 3

Jelly beans are $1.75 per pound; almonds are $3.75 per pound.