Question

A store is having a sale on trail mix and jelly beans. For 7 pounds of trail mix and 9 pounds of jelly beans, the total cost is $ 37 . For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $ 17 . Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

The cost for each pound of trail mix is $ 1.75 and each pound of jelly beans is $ 2.75.

Explanation:

Let each pound of trail mix cost
`x` dollars and each pound of jelly beans cost
`y` dollars.

Given:

7 pounds of trail mix and 9 pounds of jelly beans cost $ 37.

So,
`7x+9y=37`--------------- 1

Also, 5 pounds of trail mix and 3 pounds of jelly beans cost $ 17.

So,
`5x +3y=17`--------------- 2

Multiplying equation 2 by -3, we get

`(5x +3y=17)* -3\\-15x-9y=-51-------- 3`

Now, adding equations 1 and 3, we get

`7x+9y-15x-9y=37-51\\7x-15x=-14\\-8x=-14\\x=(-14)/(-8)=\$1.75`

Now, plug in
`x=1.75` in equation 1 and solve for
`y`.

`7(1.75)+9y=37\\12.25+9y=37\\9y=37-12.25\\9y=24.75\\y=(24.75)/(9)\\ y=\$2.75`

Therefore, the cost for each pound of trail mix is $ 1.75 and each pound of jelly beans is $ 2.75.