Answer:
The cost of bucket of popcorn is 4.25$ and The cost of fountain drinks is 6.75$
Explanation:
A movie theater sells popcorn and fountain drinks.
Let, x be the number of popcorn
and y be the number of fountain drinks.
Now,
Statement 1: Brett buys 1 popcorn and 3 fountain drinks for his family which cost him a total of $24.50
Equation 1 can be written as x+3y=24.50
Statement 2: Sarah buys 3 popcorn and 4 fountain drinks for his family which cost her a total of $39.75
Equation 2 can be written as 3x+4y=39.75
The system of equation is given by
Equation 1 : x+3y=24.50
Equation 2 : 3x+4y=39.75
Using a method of substitution,
For equation 1
x+3y=24.50
x=24.50-3y
Now, replacing the value of x in equation 2
Equation 2 is 3x+4y=39.75
3x+4y=39.75
3(24.50-3y)+4y=39.75
73.50-9y+4y=39.75
-5y=33.75
y=6.75
Putting value y in any equations
Equation 1 is x+3y=24.50
x+3y=24.50
x+3(6.75)=24.50
x+20.25=24.50
x=4.25
Thus,
The cost of bucket of popcorn is 4.25$ and The cost of fountain drinks is 6.75$