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

Answer:

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

Step-by-step 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.