Solving systems of an equation - homework due tomorrow - picture provided

The cost of bucket of popcorn is 4.25$ and The cost of fountain drinks is 6.75$

Step-by-step 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$