Question

A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $11. For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23 . Find the cost for each pound of jelly beans and each pound of trail mix.

Answer 1

the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75

Explanation:

Given A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $11. For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23 . We have to find the cost for each pound of trail mix and each pound of jelly beans.

Let the cost of each pound of trail mix is $y.

and the cost of each pound of jelly beans is $x.

According to question,

For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $11.

⇒
`3x+2y=11` → (1)

For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23

⇒
`5x+6y=23` → (2)

Solving (1) and (2), we get

3(1 equation)-(2 equation)=0

⇒
`3(3x+2y)-5x-6y=3(11)-23`

⇒
`9x+6y-5x-6y=10`

hence,

⇒
`4x=10`

⇒
`x=2.5`

Putting
`x=2.5` in
`3x+2y=11` we get ;

⇒
`3x+2y=11`

⇒
`3(2.5)+2y=11`

⇒
`2y=11-7.5=3.5`

⇒
`y=1.75`

Hence, the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75 .