Question

At the movie theater,the Clayton family bought 4 fountain drinks and 3 bags of popcorn and paid $22.75.how much is a fountain drink

Answer 1

Question:

At the movie theater , the Clayton family bought 4 fountain drinks and 3 bags of popcorn and paid $22.50.  The Hanks family bought 5 fountain drinks and 2 bags of popcorn and paid $23.75.  How much is a fountain drink?  How much is a bag of popcorn ?

Answer:

Cost of 1 fountain drink is $ 3.75 and cost of 1 bag of popcorn is $ 2.5

Solution:

Let "f" be the price of 1 fountain drink

Let "p" be the price of 1 bag of popcorn

Given that Clayton family bought 4 fountain drinks and 3 bags of popcorn and paid $22.50

4 x price of 1 fountain drink + 3 x price of 1 bag of popcorn = 22.50

$4 \times f + 3 \times p = 22.50$

4f + 3p = 22.5 -------- eqn 1

Also given that Hanks family bought 5 fountain drinks and 2 bags of popcorn and paid $23.75

5 x price of 1 fountain drink + 2 x price of 1 bag of popcorn = 23.75

$5 \times f + 2 \times p = 23.75$

5f + 2p = 23.75 -----------------eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

2(4f + 3p = 22.5)

8f + 6p = 45 -------- eqn 3

Multiply eqn 2 by 3

3(5f + 2p = 23.75)

15f + 6p = 71.25 --------- eqn 4

Subtract eqn 3 from eqn 4

15f + 6p = 71.25

8f + 6p = 45

( - ) -------------------

7f = 26.25

f = 3.75

Substitute f = 3.75 in eqn 1

4(3.75) + 3p = 22.5

15 + 3p = 22.5

3p = 22.5 - 15

3p = 7.5

p = 2.5

Thus cost of 1 fountain drink is $ 3.75 and cost of 1 bag of popcorn is $ 2.5