Justin and Lincoln go to the movie theater and purchase refreshments for their friends. Justin spends a total of $14.00 on 4 drinks and 4 bags of popcorn. Lincoln spends a total of $20.50 on 8 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

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iwillanswer iwillanswer · Answer 1 · 2019-12-28T06:34:11+01:00

4d + 4b = 14 and 8d + 3b = 20.50 are the system of equations that can be used to find the price of one drink and the price of one bag of popcorn

Price of one drink is $ 2 and price of one bag of popcorn is $ 1.5

Let "d" be the price of one drink

Let "b" be the price of one bag of popcorn

Given that Justin spends a total of $14.00 on 4 drinks and 4 bags of popcorn.

So we can frame a equation as:

4 drinks x price of one drink + 4 bags of popcorn x price of one bag of popcorn = $ 14.00

[tex]4 \times d + 4 \times b = 14.00[/tex]

4d + 4b = 14 ------ eqn 1

Given that Lincoln spends a total of $20.50 on 8 drinks and 3 bags of popcorn

So we can frame a equation as:

8 drinks x price of one drink + 3 bags of popcorn x price of one bag of popcorn = $ 20.50

[tex]8 \times d + 3 \times b = 20.50[/tex]

8d + 3b = 20.50 ---- eqn 2

Thus eqn 1 and eqn 2 are the system of equations that can be used to find the price of one drink and the price of one bag of popcorn

Let us solve eqn 1 and eqn 2 to find values of "d" and "b"

Multiply eqn 1 by 2

8d + 8b = 28 --- eqn 3

Substract eqn 2 from eqn 3

8d + 8b = 28

8d + 3b = 20.50

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

5b = 7.5

Substitute b = 1.5 in eqn 1

4d + 4(1.5) = 14

4d = 8

Thus price of one drink is $ 2 and price of one bag of popcorn is $ 1.5