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

Step-by-step 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 .