Question

Makayla and Emily go to the movie theater and purchase refreshments for their friends. Makayla spends a total of $57.00 on 6 drinks and 6 bags of popcorn. Emily spends a total of $33.00 on 4 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 drink, to the nearest cent.

Answer 1

A drink costs $4.50 and a bag of popcorn costs $5.00.

Explanation:

The system would be:

`6d+6p=57\\4d+3p=33\\`

I'll be using the subtraction method first, to find d (price of a drink):

`+6d+6p=+57\\-8d-6p=-66\\--------\\-2d=-9\\\\2d=9\\d=4.5`

Now, we substitute in and solve for p:

`6(4.5)+6p=57\\27+6p=57\\6p=30\\p=5`

Finally, we use the second equation to check the values:

`4(4.5)+3(5)=33\\18+15=33\\33=33`

So:

`\left \{ {{d=4.5} \atop {p=5}} \right.`