Totally lost, please help

Question

At the local convenience store, 7 bags of chips and 3 containers of dip cost $33. However, 3 bags of chips and 4 containers of dip cost $25. What is the cost of one bag of chips and one container of dip?

Answer 1

Use the following variables.

b: number of bags

c: number of containers

 

Then we know the following must both be true.

7b+3c = 33

3b+4c = 25

 

Now we solve the system of equations. I will multiply first equation by 4 and second equation by 3.

28b+12c = 132

9b + 12c = 75

 

We can now eliminate terms with c by subtracting equations.

19b = 57

 

Thus, b=3. We can now determine c.

3(3)+4c = 25

4c = 16

c = 4

 

So, bags are $3 and containers are $4. Let's check...

 

7(3)+3(4) = 33, check
3(3)+4(4) = 25, check

 

Yay!