system of equations question

Question

You purchase a drink and sandwich for $4.50. Your friend purchases a drink and 5 sandwiches for $16.50. Determine the price of both the drink and sandwich.

Answer 1

Let price of a drink = x

Let price of a sandwich = y

 

Set up equations.

 

x + y = 4.50           eq1

x + 5y = 16.50        eq2

 

 

Substitute eq1 into eq2.  We will have eq2 in terms of y.

 

4.50 - y + 5y = 16.50

4.50 + 4y = 16.50

           4y = 12

             y = 3

 

Substitute this value into eq1.

 

x = 4.50 - y

x = 4.50 - 3

x = 1.50

 

The price of a drink is $1.50 and the price of a sandwich is $3.00