Question

A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and

7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:

Answer 1

Cost for each pound of jelly beans: $2.75

Cost for each pound of almonds: $3.75

Explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

`\implies 3J + 5A = 27`

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

`\implies 9J + 7A = 51`

Therefore, the system of equations is:

`\begin{cases}3J+5A=27\\9J+7A=51\end{cases}`

To solve the system of equations, multiply the first equation by 3 to create a third equation:

`3J \cdot 3+5A \cdot 3=27 \cdot 3`

`9J+15A=81`

Subtract the second equation from the third equation to eliminate the J term.

`\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\frac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\frac12} &&&8A&=&30\end{array}`

Solve the equation for A by dividing both sides by 8:

`(8A)/(8)=(30)/(8)`

`A=3.75`

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

`3J+5(3.75)=27`

`3J+18.75=27`

`3J+18.75-18/75=27-18.75`

`3J=8.25`

`(3J)/(3)=(8.25)/(3)`

`J=2.75`

Therefore, the cost of one pound of jelly beans is $2.75.