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:

Almonds = $2.25/pound

Jelly Beans = $3.25/pound

Step-by-step 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

Answer 2

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.

Step-by-step explanation: