Question

Jason and Henry go to the movie theater and purchase refreshments for their friends.

Jason spends a total of $66.75 on 12 drinks and 1 bag of popcorn.

Henry spends a total of $82.50 on 3 drinks and 10 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.


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Answer 1

Part 1) The system of equations is equal to

12x+y=66.75

3x+10y=82.50

Part 2) The cost of one drink is $5

Explanation:

Part 1) Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn

Let

x----> the price of one drink

y ----> the price of one bag of popcorn

we know that

Jason

12x+y=66.75 -----> equation A

Henry

3x+10y=82.50 -----> equation B

Part 2) Using these equations, determine and state the price of a drink, to the nearest cent

12x+y=66.75 -----> equation A

3x+10y=82.50 -----> equation B

Solve the system of equations by elimination

Multiply the equation A by -10 both sides

-10*(12x+y)=66.75*(-10)

-120x-10y=-667.5 -----> equation C

Adds equation B and C and solve for x

3x+10y=82.50

-120x-10y=-667.5

-----------------------------

3x-120x=82.50-667.5

120x-3x=667.50-82.50

117x=585

x=5

therefore

The cost of one drink is $5