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 h be the number of hamburgers purchased and let m be the number of milkshakes purchased.

The total bill for the 12 items can be represented by the equation:

1.50h + 2.00m = 21.50

Since there are a total of 12 items, the total number of items equation is:

h + m = 12

Therefore, the system of equations is:

1.50h + 2.00m = 21.50
h + m = 12

To solve this system of equations, we can multiply the second equation by 1.50 to eliminate h when adding the equations together:

1.50h + 2.00m = 21.50
1.50h + 1.50m = 18.00

Now, subtract the second equation from the first:

0.50m = 3.50
m = 7

Substitute m = 7 back into the second equation:

h + 7 = 12
h = 5

Therefore, your group bought 5 hamburgers and 7 milkshakes.