Question

3. 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.

From the given information, we can create a system of equations:

1.50x + 2.00y = 21.50 (total cost of 12 items)
x + y = 12 (total number of items)

Solving this system of equations, we can use the substitution method:

From the second equation, we can rewrite it as x = 12 - y. Then substitute this expression into the first equation:

1.50(12 - y) + 2.00y = 21.50
18 - 1.50y + 2.00y = 21.50
0.50y = 3.50
y = 7

Substitute y = 7 back into x = 12 - y:

x = 12 - 7
x = 5

Therefore, your group bought 5 hamburgers and 7 milkshakes for lunch.