For 5 lb of jelly beans and 3 lb of almonds the total cost is $15 For 2 lb of jelly beans & 6 lb of almonds the total cost is $12 Find the cost for each pound of jelly beans and each pound of almonds

Question

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

Answer 1

You can solve this using a system of equations by substitution or elimination.

Let x = jelly beans

Let y = almonds

Equation 1

5x + 3y = 15

Equation 2

2x + 6y = 12

Multiply Equation 1 by negative 2 to give

-10x - 6y = -30

Add this to Equation 2 to eliminate y

-10x - 6y = -30

2x + 6y = 12

The y is eliminated leaving

-8x = -18

Divide both sides by negative 8 to give

x = 2.25

Substitute this value back into Equation 2 to solve for y

2x + 6y = 12

2(2.25) + 6y =12

4.50 + 6y = 12

Subtract 4.50 from both sides of the equation to give

6y = 7.50

Divide both sides by 6 to solve for y

y = 7.50/6

y= 1.25

Jellybeans are $2.25 per pound

Almonds are $1.25 per pound

You can check these values in both equations

5(2.25) + 3(1.25) = 15

11.25 + 3.75 = 15

And

2(2.25) + 6(1.25) = 12

4.50 + 7.50 = 12

You can also try using Substitution instead of Elimination with the equations above. Notice also that Equation 2

2x + 6y = 12 is divisible by 2 and also says that 1 lb of jellybeans and 3 lbs of almonds costs $6.

Since you are dealing with cost, decimals will be involved.

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