answer for class

Question

A store is having a sale on chocolate chips and walnuts. For 7 pounds of chocolate chips and 9 pounds of walnuts, the total cost is $53. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $25. Find the cost for each pound of chocolate chips and each pound of walnuts.

Answer 1

These really used to get me. Let's see if we can figure this one out.

7c + 9w = 53

5c + 3w = 25

Ok, now what?? Well, first off, know that we can add these two equations together. We'd end up with 12c + 12w = 78.

Another thing we can do is multiply an equation by a constant and it won't change the graph. Let's multiply the top equation by 100 for fun. 700c + 900w = 5300.

My point in showing both of these is that we want our two equations to have opposite coefficients in one of the variables so that we add the equations together and one variable cancels out. We can multiply one or both of our equations by any constant, though not even the same constant for each.

Let's look at what we have. What I notice is that we can multiply the bottom equation by -3 to get -9w. Works for me!

7c + 9w = 53

-15c - 9w = -75

Now, when we add the equations together, we get...

-8c = -22

c = 2.75

Ok, one pound of chocolate chips costs $2.75. Now, substitute into either equation.

7(2.75) + 9w = 53

19.25 + 9w = 53

9w = 33.75

w = 3.75

One pound of walnuts costs $3.75.

Boom.