Question

You and some friends buy hamburgers and milkshakes for lunch. A hamburger costs $1.50 and a milkshake costs $2.00.The total bill for 12 items is $21.50.How many hamburgers and how many milkshakes did your group buy? Write a system of equations to model this situation. Solve by any method. (even if you use graphing, make sure to write the equations in the system).

Answer 1

Let x be the number of hamburgers purchased and y be the number of milkshakes purchased.

The cost equation is:
1.50x + 2.00y = 21.50

The quantity equation is:
x + y = 12

Therefore, the system of equations is:
1.50x + 2.00y = 21.50
x + y = 12

Solving the system by substitution method:
x = 12 - y
1.50(12 - y) + 2.00y = 21.50
18 - 1.50y + 2.00y = 21.50
0.50y = 3.50
y = 7

Plugging y back into x = 12 - y:
x = 12 - 7
x = 5

Therefore, your group bought 5 hamburgers and 7 milkshakes.