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?
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.