Question

A store is having a sale on jelly beans and almonds. For two almonds of jellybeans and 5 pounds of almonds the total cost is $10. For 8 pounds of jellybeans and 3 pounds of almonds, the total cost is $23. Find the cost for each pound of jellybeans and each pound of almonds

Answer 1

Answer: the cost of each pound of jellybeans is $2.5

the cost of each pound of almonds is $1

Explanation:

Let x represent the cost of each pound of jellybeans.

Let y represent the cost of each pound of almonds.

For two pounds of jellybeans and 5 pounds of almonds the total cost is $10. It means that

2x + 5y = 10- - - - - - - - -1

For 8 pounds of jellybeans and 3 pounds of almonds, the total cost is $23. It means that

8x + 3y = 23- - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 1, it becomes

8x + 20y = 40

8x + 3y = 23

Subtracting, it becomes

17y = 17

y = 17/17

y = 1

Substituting y = 1 into equation 1, it becomes

2x + 5 × 1 = 10

2x + 5 = 10

2x = 10 - 5 = 5

x = 5/2 = 2.5

Answer 2

The answer to your question is almonds = $1, jelly beans = $2.5

Explanation:

Data

2 pounds of jelly beans and 5 pounds of almonds = $10

8 pounds of jelly beans and 3 pounds of almonds = $23

jelly beans = j

almonds = a

Process

1.- Write two equations to solve this problem

2j + 5a = 10 Equation l

8j + 3 a = 23 Equation ll

2.- Solve the system of equations by elimination

-Multiply equation l by -4

-8j - 20a = -40

8j + 3 a = 23

-Simplify

0 - 17 a = -17

a = -17/-17

a = 1

-Find j

8j + 3(1) = 23

8j + 3 = 23

8j = 23 - 3

8j = 20

j = 20/8

j = 2.5

3.- Conclusion

The pound of almonds costs $1 and the pound of jelly beans costs $2.5