Taylor and Nora go to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks and 4 bags of popcorn Nora spends a total of $96.00 on 12 drinks and bag 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 .

System of equations also known as simultaneous equation is:

6x + 4y = $69

12x + y = $96

The cost of a drink using the simultaneous equation above is $7.50

Step-by-step explanation:

Let x represent the cost of a drink at the movie theater

Let y represent the cost a bag of popcorn at the movie theater

Taylor purchases 6 drinks and 4 bags of popcorn with a total of $69. Mathematically, this means:

6x + 4y = $69 (eqn 1)

Nora purchases 12 drinks and 1 bag of popcorn with a total of $96. Mathematically, this means:

12x + 1y = $96 (eqn 2)

Combining these two equations, we have a simultaneous equation that can be used to determine the cost of each drink and bag of popcorn. We use elimination method to solve for x and y in the equations.

We multipy (eqn 1) by 2 and (eqn 2) by 1 in order to make the x variables in both equations equal. We have

2 × 6x + 4y = $69

1 × 12x + 1y = $96

Eqn 1 and 2 becomes

12x + 8y = 138 (eqn 3)

12x + 1y = 96 (eqn 4)

Next, we subtract eqn 4 from eqn 3 to have:

7y = 42

y = 6

Since y=6, we substitute the value of y into eqn 1

6x + 4y = 69

6x + 4(6) = 69

6x + 24 = 69

6x = 69 - 24

6x = 45

Divide both sides by 6

x = 7.5

The cost of one drink denoted by x is $7.5 while the cost of one bag of popcorn denoted by y is $6.