Question

A store is having a sale on jelly beans and trail mix. For 9 pounds of jelly beans and 7 pounds of trail mix, the total cost is $42. For 3 pounds of jelly beans and

5 pounds of trail mix, the total cost is $24. Find the cost for each pound of jelly beans and each pound of trail mix.
X
5
Cost for each pound of jelly beans: $
Cost for each pound of trail mix: $

Answer 1

Cost of each pound of jelly beans = US$ 1.75

Cost of each pound of trail mix = US$ 3.75

Explanation:

1. Let's review the information given to answer the question correctly:

Cost of 9 pounds of jelly beans + 7 pounds of trail mix = US$ 42

Cost of 3 pounds of jelly beans + 5 pounds of trail mix = US$ 24

2. Let's find the cost for each pound of jelly beans and each pound of trail mix.

x = Cost of a pound of jelly beans

y = Cost of a pound of trail mix

9x + 7y = 42

3x + 5y = 24

Let's solve for x on the 1st equation:

9x + 7y = 42

9x = 42 - 7y

x = 42/9 - 7y/9

Let's solve for y on the 2nd equation:

3x + 5y = 24

3 (42/9 - 7y/9) + 5y = 24 (Replacing x)

42/3 - 7y/3 + 5y = 24

14 - 7y/3 + 5y = 24

-7y/3 + 5y = 24 -14

-7y/3 + 5y = 10

-7y +15y = 30

8y = 30

y = 30/8 = 15/4 = 3 3/4 = 3.75

Substitution of y on the 1st equation

9x + 7y = 42

9x + 7 * 15/4 = 42

9x + 105/4 = 42

9x = 42 - 105/4

36x = 168 - 105 (Multiplying by 4)

36x = 63

x = 63/36 = 21/12 = 7/4 = 1.75