# How do I find the price of two things when given the price with both added together? Here's the math problem.The difference in cost between a large bag of chips and a small bag of chips was 90¢....

How do I find the price of two things when given the price with both added together? Here's the math problem.

The difference in cost between a large bag of chips and a small bag of chips was 90¢. Alicia bought 5 large bags and 3 small bags of chips for her party and spent $17.22. What was the cost of a small bag of chips?

*print*Print*list*Cite

### 3 Answers

Let the price of the small bag be x and the price of the big bag be y.

Given that the difference in cost is 0.90

==> y - x = 0.90 ............(1)

Now the cost of 5 large bags and 3 small bags is 17.22.

==> 3x + 5y = 17.22...........(2)

Then we have 2 equations with 2variables.

We will use the substitution method to solve for x.

From (1) y= x+ 0.90.

Then we will substitute into (2).

==> 3x + 5(x+.90) = 17.22

==> 3x + 5x + 4.5 = 17.22

==> 8x = 17.22 - 4.5

==> 8x = 12.72

==> x = 1.59

**Then the small bag costs $1.59 .**

Let the small bag of chips cost S and the large bag of chips cost L.

The difference in the cost of the two is $0.9

=> L = S + 0.9

Alicia bought 5 large and 3 small bags for $17.22

=> 5L + 3S = 17.22

=> 5(S + 0.9) + 3S = 17.22

=> 5S + 4.5 + 3S = 17.22

=> 8S = 12.72

=> S = 12.72/8

=> S = 1.59

**The cost of the small bag of chips is $1.59.**

We'll have to parse each statement so it makes sense mathematically:

L = large S = small

The difference in cost between a large bag of chips and a small bag of chips was 90¢.

L - S = .90

Alicia bought 5 large bags and 3 small bags of chips for her party and spent $17.22.

5L + 3S = 17.22

We want to find the cost of the small bag. We can do this by solving this system of equations.