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A movie theater sells popcorn and fountain drinks. Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50. Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75. If p represents the number of popcorn buckets and d represents the number of drinks, then the system of equations

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tutorAnne

Answer: the systems of equations to solve the unit price  of popcorn and rinks are

1 p + 3 d= 12.50---- equation 1

3 p + 4 d=  23.75 ---- equation 2

The price of A popcorn bucket  = $4.25 and price of 1 fountain  drink = $2.75

Step-by-step explanation:

Step 1

If p represents the number of popcorn buckets

and d represents the number of drinks,

The expression that  Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50 becomes

1 p + 3 d= $12.50

and The expression that Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75 becomes

3 p + 4 d=  $23.75

such that the systems of equations to solve the unit prices of popcorn and drinks are

1 p + 3 d= $12.50---- eqn 1

3 p + 4 d=  $23.75 ---- eqn 2

Step 2

1 p + 3 d= $12.50---- eqn 1

3 p + 4 d=  $23.75 ---- eqn 2

Multiplying equation 1 by( 3 )

1 p + 3 d= $12.50---- eqn 1 x 3

3p+ 9d= 37.5----- equation 3

and subtracting equation 2 from  equation 3  becomes

3p+ 9d= 37.5----- equation 3

- 3 p + 4 d=  $23.75

5d= 13.75

d= 13.75/5

d= 2.75

to find p, sinceaa d = 2.75,

1 p + 3 d= 12.50

1 p + 3  x 2.75= 12.50

p= 12.50-8.25

p=4.25

THerefore the price of popcorn = $4.25 and price of drinks = $2.75

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