Respuesta :
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
[tex]4 \times f + 3 \times p = 22.50[/tex]
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
[tex]5 \times f + 2 \times p = 23.75[/tex]
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
