You are selling hot dogs
and sodas. Each hot dog
costs $1.50 and each soda
costs $0.50. At the end of
the night you made a total of
$78.50. A total of 87 hot
dogs and sodas combine
were sold. How many hot
dogs were sold and sodas
were sold? Write a linear
system of equations that can
be used to solve this
problem. Then
Then what? I can’t see the rest.
h+s = 87
1.50h + 0.50s = 78.50
Let's define two variables to represent the number of hot dogs sold and the number of sodas sold.
Let "x" represent the number of hot dogs.
Let "y" represent the number of sodas.
The cost of each hot dog is $1.50, so the total revenue from hot dogs can be found by multiplying the number of hot dogs sold (x) by the cost of each hot dog ($1.50):
Revenue from hot dogs = 1.50 * x
Similarly, the total revenue from sodas can be found by multiplying the number of sodas sold (y) by the cost of each soda ($0.50):
Revenue from sodas = 0.50 * y
The total revenue from both hot dogs and sodas is given as $78.50:
Total Revenue = Revenue from hot dogs + Revenue from sodas
Substituting the expressions for revenue from hot dogs and sodas, we have:
78.50 = 1.50 * x + 0.50 * y
Since the total number of hot dogs and sodas sold is given as 87, we can write another equation:
Total Quantity = Number of hot dogs + Number of sodas
Substituting the variables, we have:
87 = x + y
So, the linear system of equations that can be used to solve this problem is:
1.50x + 0.50y = 78.50 (Equation 1)
x + y = 87 (Equation 2)
You can solve this system of equations using various methods, such as substitution or elimination, to find the values of x and y, which represent the number of hot dogs and sodas sold, respectively.