Question

Your class raised money by selling hot dogs and hamburgers. Hot dogs were sold for $.50 (fifty cents), and hamburgers were sold for $1 (one dollar). The total money raised by your class was $80. Together you sold 108 hot dogs and hamburgers. How many of each were sold?

Answer 1

Answer:

Number of hot dogs sold =  56

Number of  hamburgers sold = 52

Step-by-step explanation:

Let

Number of hot dogs sold = x

Number of  hamburgers sold = y

We can make equation from given equations:

$0.50x+1y=80$ (Hot dogs were sold for $.50 (fifty cents), and hamburgers were sold for $1 (one dollar). The total money raised by your class was $80. )

$x+y=108$  (Together you sold 108 hot dogs and hamburgers.)

Now we cam solve these system of equations to find value of x and y

$0.50x+y=80--eq(1)\\x+y=108--eq(2)$

Subtract both equations to get value of x:

$0.50x+y=80\\x\:\:\:\:\:\:\:\: + y=108\\-\:\:\:\:\:\:\:\: -\:\:\:\:\:\: -\\---------\\-0.5x=-28\\x=\frac{-28}{-0.5}\\x=56$

We get value of x = 56

Now putting value of x in equation 2 to find value of y

$x+y=108\\56+y=108\\y=108-56\\y=52$

So, we get y = 52

Therefore,

Number of hot dogs sold = x = 56

Number of  hamburgers sold = y = 52