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.
Linear equation in two variables can be defined as an equation in the form:
[tex]\rm ax + by = c[/tex] , 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:
[tex]\rm 3s +2c = 22[/tex]
The cost of two sandwiches and one chips bag is $14.25.
Therefore, the 2nd equation will be:
[tex]\rm 2s + c = 14.25[/tex]
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:
[tex]\begin{aligned}\rm 2s + c &= 14.25\\\\c &= 14.25 - 2s\end[/tex] ... (3)
Now we will put [tex]\rm c = 14.25 - 2s[/tex] in equation 1:
[tex]\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[/tex]
On substituting the value of s in equation 3:
[tex]\rm c = 14.25 - 2s \\\\c = 14.25 - 2(6.50)\\\\c = 14.25 - 13\\\\c = \$1.25[/tex]
Therefore the cost of a bag of chips is $1.25.
Learn more about linear equations in two variables here:
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