Question

Easton and Eli go to the movie theater and purchase refreshments for their friends.

Easton spends a total of $118.50 on 9 bags of popcorn and 6 drinks.

Eli spends a total of $83.50 on 3 bags of popcorn and 10 drinks.

Write a system of equations that can be used to find the price of one bag of popcom
and the price of one drink.

Using these equations, determine and state the price of a bag of popcorn, to the
nearest cent.

Answer 1

Price of one bag of popcorn: $9.5

Price of one drink: $5.5

Explanation:

Let be "b" the price in dollars of a bag of popcorn and "d" the price in dollars of a drink.

You know that the total amount of money Easton spends on on 9 bags of popcorn and 6 drinks, is $118.50. Then,this can be represented with the following equation:

`9b+6d=118.50`

Knowing that Eli spends $83.50 on 3 bags of popcorn and 10 drinks, you can write the second equation:

`3b+10d=83.50`

Then, the System of equations is:

`\left \{ {{9b+6d=118.50} \atop {3b+10d=83.50}} \right.`

You can use the Elimination methot to solve it:

1. Multiply the second equation by -3.

2. Add both equations.

3. Solve for "d"

Then, you get:

`\left \{ {{9b+6d=118.50} \atop {-9b-30d=-250.5}} \right\\............................\\-24d=-132\\\\d=5.5`

4. You can subsitute "d" into the second equation and solve for "b":

`3b+10(5.5)=83.50\\\\3b=83.50-55\\\\b=9.5`