Question

At a fast food restaurant, three chicken sandwiches and two small orders of fries cost $8.87. Five chicken sandwiches and four small orders of fries cost $15.55. How much does each item cost?

Answer 1

The cost of each chicken sandwich is $2.19 and the cost of each small orders of fries is $1.15.

Explanation:

Given:

The cost of three chicken sandwiches and two small orders of fries is $8.87. And the cost of five chicken sandwiches and four small orders of fries is $15.55.

Now, to find the cost of each chicken sandwiches and each small orders of fries.

Let the cost of each chicken sandwich be
`x.`

And let the cost of each small orders of fries be
`y.`

So, the total cost of three chicken sandwiches and two small orders of fries:

`3x+2y=8.87` ......(1)

Now, the total cost of five chicken sandwiches and four small orders of fries:

`5x+4y=15.55` .......(2)

Now, to solve the equations by using elimination method:

`3x+2y=8.87` ....(1)

`5x+4y=15.55` .....(2)

So, multiplying equation (1) by 2 we get:

`6x+4y=17.74`

And, then subtracting equation (2) from the resulting equation (1):

`(6x+4y)-(5x+4y)=17.74-15.55\\\\6x+4y-5x-4y=2.19\\\\6x-5x+4y-4y=2.19\\\\x=2.19.`

The cost of each chicken sandwich = $2.19.

Now, substituting the value of
`x` in equation (1):

`3x+2y=8.87\\\\3(2.19)+2y=8.87\\\\6.57+2y=8.87`

Subtracting both sides by 6.57 we get:

`2y=2.3`

Dividing both sides by 2.3 we get:

`y=1.15.`

The cost of each small orders of fries = $1.15.

Therefore, the cost of each chicken sandwich is $2.19 and the cost of each small orders of fries is $1.15.