Question

If three sandwiches and two bags of chips cost $22. 00, and two sandwiches and one bag of chips cost $14. 25, how much does a bag of chips cost?.

Answer 1

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.

What is a linear equation in two variables?

Linear equation in two variables can be defined as an equation in the form:

$\rm ax + by = c$ , 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:

$\rm 3s +2c = 22$                              

The cost of two sandwiches and one chips bag is $14.25.

Therefore, the 2nd equation will be:

$\rm 2s + c = 14.25$

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:

$\begin{aligned}\rm 2s + c &= 14.25\\\\c &= 14.25 - 2s\end$                                   ... (3)

Now we will put  $\rm c = 14.25 - 2s$  in equation 1:

$\begin{aligned} \rm 3s + 2c &= 22\\\\3s + 2(14.25 - 2s) &= 22\\\\3s + 28.50 - 4s &= 22\\\\-s + 28.50 &= 22\\\\s &= 28.50 - 22\\\\s &= \ 6.50\end$

On substituting the value of s in equation 3:

$\rm c = 14.25 - 2s \\\\c = 14.25 - 2(6.50)\\\\c = 14.25 - 13\\\\c = \ 1.25$

Therefore the cost of a bag of chips is $1.25.

Learn more about linear equations in two variables here:

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