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

Answer:

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

Step-by-step 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

$(5x +3y=17)\times -3\\-15x-9y=-51-------- 3$

Now, adding equations 1 and 3, we get

$7x+9y-15x-9y=37-51\\7x-15x=-14\\-8x=-14\\x=\frac{-14}{-8}=\ 1.75$

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

$7(1.75)+9y=37\\12.25+9y=37\\9y=37-12.25\\9y=24.75\\y=\frac{24.75}{9}\\ y=\ 2.75$

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