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 [tex]x[/tex] dollars and each pound of jelly beans cost [tex]y[/tex] dollars.
Given:
7 pounds of trail mix and 9 pounds of jelly beans cost $ 37.
So, [tex]7x+9y=37[/tex]--------------- 1
Also, 5 pounds of trail mix and 3 pounds of jelly beans cost $ 17.
So, [tex]5x +3y=17[/tex]--------------- 2
Multiplying equation 2 by -3, we get
[tex](5x +3y=17)\times -3\\-15x-9y=-51-------- 3[/tex]
Now, adding equations 1 and 3, we get
[tex]7x+9y-15x-9y=37-51\\7x-15x=-14\\-8x=-14\\x=\frac{-14}{-8}=\$1.75[/tex]
Now, plug in [tex]x=1.75[/tex] in equation 1 and solve for [tex]y[/tex].
[tex]7(1.75)+9y=37\\12.25+9y=37\\9y=37-12.25\\9y=24.75\\y=\frac{24.75}{9}\\ y=\$2.75[/tex]
Therefore, the cost for each pound of trail mix is $ 1.75 and each pound of jelly beans is $ 2.75.
