Question

Louis bought a burger and soda for $8. Kate purchased a slice of pizza and soda for $9. David purchased a burger, a slice of pizza, and a soda for $13.50. Write equations for each purchase. Solve your equations to find the cost of a burger, slice of pizza and a soda.

Answer 1

cost of a burger= $4.5

Cost of soda = $3.5

Cost of a slice of pizza = $5.5

Explanation:

Let x = the cost of a burger.

Let y = the cost of a soda.

Let z = the cost of a slice of pizza.

Louis bought a burger and soda for $8. This means

x + y = 8 - - - - - - - -1

Kate purchased a slice of pizza and soda for $9. This means

z + y = 9 - - - - - - - - - 2

David purchased a burger, a slice of pizza, and a soda for $13.50. This means

x + y + z = $13.50 - - - - - - - 3

Substituting x = 8-y and z = 9-y in equation 3, it becomes

8-y + y + 9-y = 13.50

-y -y + y = 13.50 -8-9

-y = -3.5

y = $3.5

Put y = 3.5 in equation 1

x + 3.5 = 8

x = 8 - 3.5 = $4.5

Put x = 4.5 and y = 3.5 in equation 3.

4.5 + 3.5 + z = 13.5

8 + z = 13.5

z = 13.5 - 8 = $5.5