Question

A store is having a sale on walnuts and chocolate chip.s For 3 pounds of walnuts and 2 pounds of chocolate chips. the total cost is $14. for 8 pounds of walnuts and 4 pounds of chocolate chips, the total cost is $33. find the cost for each pound of walnuts and each pound of chocolate chips.

Answer 1

x= walnut cost per pound
y= chocolate chips cost per pound

3x+2y=$14
8x+4y=$33

There are a couple ways to solve this: substitution method or elimination method. I'm going to use the elimination method.

To add both equations together, we must cancel out one of the variables.

We can multiply the whole first equation by (-2) to cancel out the y variable:
3x+2y=$14
(-2)(3x)+(-2)(2y)=(-2)(14)
-6x-4y=-28

Add second equation to new first equation (y will cancel out):
-6x-4y=-28
8x+4y=$33
2x=5
Divide both sides by 2
x= $2.50 walnut cost per pound

Substitute to find y:
3x+2y=14
3(2.50)+2y=14
7.50+2y=14
Subtract 7.50 from both sides
2y=6.50
Divide both sides by 2
y= $3.25 chocolate chip cost per lb.

Check:
8x+4y=33
8(2.50)+4(3.25)=33
20+13=33
33=33

Hope this helps! :)