Question

A store is having a sale on almonds and jelly beans. For 5 pounds of almonds and 3 pounds of jelly beans, the total cost is $21. For 2 pounds of almonds and 6 pounds of jelly beans, the total cost is $24 . Find the cost for each pound of almonds and each pound of jelly beans.

Answer 1

Answer: Let x = number of pounds of jelly beans

y = number of pounds of almonds.

Then, 4x + 8y = 33

2x + 3y = 13

Multiply the second equation by -2 to get the system:

4x + 8y = 33

-4x - 6y = -26

Adding the equations, we get 2y = 7. So, y = 3.5

Substitute for y in either of the given equations: 2x + 3(3.5) = 13

2x + 10.5 = 13

2x = 2.5

x = 1.25

ANSWER: a pound of jelly beans costs $1.25 and a pound of almonds costs $3.50.

Explanation:

Answer 2

Almonds = $2.25/pound

Jelly Beans = $3.25/pound

Explanation:

5a + 3b = 21 eq. 1

2a + 6b = 24 eq. 2

By multiplying by -2 the eq. 1

-10a - 6b = -42

By adding this last value with eq. 2

-10a - 6b = -42

2a + 6b = 24

-8a + 0b = -18

-8a = -18

a = -18/-8

a = 2.25

from eq. 1:

5*2.25 + 3b = 21

11.25 + 3b = 21

3b = 21 - 11.25

3b = 9.75

b = 9.75/3

b = 3.25

Check:

from eq. 2

2*2.25 + 6*3.25 = 24

4.5 + 19.5 = 24