A bag of chips will cost $1.25. The price is calculated by making linear equations in two variables and solving them by substitution method.
<h3>What is a linear equation in two variables?</h3>
Linear equation in two variables can be defined as an equation in the form:
, where x and y are variables and a and b are not equal to 0.
For the given problem, let "s" be the cost of a sandwich and "c" be the cost of a chips bag.
Given:
The cost of three sandwiches and two chips bags is $22.00.
Therefore, the 1st equation will be:
The cost of two sandwiches and one chips bag is $14.25.
Therefore, the 2nd equation will be:
![\rm 2s + c = 14.25](https://tex.z-dn.net/?f=%5Crm%202s%20%2B%20c%20%3D%2014.25)
To calculate the cost of a chips bag, we need to solve equation 1 and equation 2 by the substitution method.
From equation 2, the value of c will be:
... (3)
Now we will put
in equation 1:
![\begin{aligned} \rm 3s + 2c &= 22\\\\3s + 2(14.25 - 2s) &= 22\\\\3s + 28.50 - 4s &= 22\\\\-s + 28.50 &= 22\\\\s &= 28.50 - 22\\\\s &= \$6.50\end](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Crm%203s%20%2B%202c%20%26%3D%2022%5C%5C%5C%5C3s%20%2B%202%2814.25%20-%202s%29%20%26%3D%2022%5C%5C%5C%5C3s%20%2B%2028.50%20-%204s%20%26%3D%2022%5C%5C%5C%5C-s%20%2B%2028.50%20%26%3D%2022%5C%5C%5C%5Cs%20%26%3D%2028.50%20-%2022%5C%5C%5C%5Cs%20%26%3D%20%5C%246.50%5Cend)
On substituting the value of s in equation 3:
![\rm c = 14.25 - 2s \\\\c = 14.25 - 2(6.50)\\\\c = 14.25 - 13\\\\c = \$1.25](https://tex.z-dn.net/?f=%5Crm%20%20c%20%3D%2014.25%20-%202s%20%5C%5C%5C%5Cc%20%3D%2014.25%20-%202%286.50%29%5C%5C%5C%5Cc%20%3D%2014.25%20-%2013%5C%5C%5C%5Cc%20%3D%20%5C%241.25)
Therefore the cost of a bag of chips is $1.25.
Learn more about linear equations in two variables here:
brainly.com/question/84787