Question

A store is having a sale on almonds and jelly beans. For 3 pounds of almonds and 8 pounds of jelly beans, the total cost is $23. For 5 pounds of almonds and 2 pounds of jelly beans, the total cost is S10. Find the cost for each pound of almonds and each pound of jelly beans.Cost for each pound of almonds: Cost for each pound of jelly beans:Solve by using system of linear equations.

Answer 1

We have to find the price of each pound of almonds and jelly beans.

We can call:

• A: price per pound of the almonds

,

• J: price per pound of the jelly beans

We know that 3 pounds of almonds and 8 pounds of jelly beans cost $23.

This means that the cost of the almonds, equal to quantity times price, and the cost of the jelly beans together is equal to $23.

We can write this as:

`3A+8J=23`

We also know that 5 pounds and 2 pounds of jelly beans cost $10. We can write this as:

`5A+2J=10`

We can substract the first equation of 4 times the second equation and it will let us solve for A:

`\begin{gathered} 4(5A+2J)-(3A+8J)=4*10-23 \\ 20A+8J-3A-8J=40-23 \\ (20-3)A+(8-8)J=17 \\ 17A=17 \\ A=(17)/(17) \\ A=1 \end{gathered}`

Knowing the price of the almonds (A = 1) we can use any of the original equations to find J:

`\begin{gathered} 5A+2J=10 \\ 5*1+2J=10 \\ 2J=10-5 \\ 2J=5 \\ J=(5)/(2) \\ J=2.5 \end{gathered}`

Answer:

Cost for each pound of almonds: $1

Cost for each pound of jelly beans: $2.50