Question

Adam and Ian go to the movie theater and purchase refreshments for their friends. Adam spends a total of $62.75 on 2 drinks and 7 bags of popcorn. Ian spends a total of $43.00 on 4 drinks and 4 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 drink, to the nearest cent.

Answer 1

Explanation:

2343get4g5g3g3

Answer 2

The cost of one drink is $2.5 and the cost of one bag of popcorn is $8.25

Explanation:

Consider the provided information.

Let price of one drink is x and the price of one bag of popcorn is y.

Adam spends a total of $62.75 on 2 drinks and 7 bags of popcorn.

`2x+7y=62.75`

`2x=62.75-7y`......(1)

Ian spends a total of $43.00 on 4 drinks and 4 bags of popcorn.

`4x+4y=43.00`

Now use substitute the value of 2x in above equation.

`2(62.75-7y)+4y=43.00`

`125.5-14y+4y=43.00`

`-10y=43.00-125.5`

`10y=82.5`

`y=8.25`

Hence the value of y is $8.25

Now find the value of x as shown:

`2x=62.75-7(8.25)`

`2x=5`

`x=2.5`

Hence, the cost of one drink is $2.5 and the cost of one bag of popcorn is $8.25