A store is having a sale on jelly beans and almonds. For 2 pounds of jellybeans and 6 pounds of almonds the total cost is $12. For 5 pounds of jellybeans and 3 pounds of almonds the total cost is $15. Find the cost for each pound of jellybeans in each pound of find the cost for each pound of jellybeans in each pound of almonds

1 pound of jellybeans costs $2.25

and 1 pound of almond costs $1.25

Step-by-step explanation:

Say jellybeans is j and almonds is a. The question can be interpreted as

2j + 6a = 12 equation 1

5j + 3a = 15 equation 2

Using elimination method for the above simultaneous equation, lets multiply equation 1 by the coefficient of j in equation 2 and vice versa

(2j + 6a = 12)*5 eqn 3

(5j + 3a = 15)*2 eqn 4

Then we will have

10j + 30a = 60 eqn 5

10j + 6a   = 30 eqn 6

Subtract equation 6 from equation 5 to eliminate j, we will have

24a = 30

Divide both side by 24, we will have

a = 30/24

a = 1.25

Therefore 1 pound of almonds cost $1.25

To get the price of jellybeans, we substitute for a in any of the equations above

2j + 6a = 12

2j + 6(1.25) = 12

2j + 7.5 = 12        Collecting the like terms, we will have

2j = 12 - 7.5

2j = 4.5               Divide both sides by 2, we will have

j = 2.25

Therefore the cost of 1 pound jellybeans is $2.25

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