Question

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 .

Answer 1

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

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.

Answer 2

The system if equation that can be used to derive this are

6x + 4y = 69 AND

12x + y = 96

The price of a drink is $7.5

Explanation:

The question here says that Taylor and Nora went 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.And we are now told to 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,we should determine and state the price of a drink, to the nearest cent .

Now, Let's assume that the price of a drink is "X" and that of a bag of popcorn to be Y

The first person made a purchase which led to the equation

6x + 4y = 69______ equation 1

And the second person also made a purchase that lead to the equation

12x + y = 96_____ equation 2

We make y the subject of the formula in equation 2 and apply it in 1

Y = 96 - 12x

Now apply the above in equation 1

6x + 4y = 69

6x + 4(96 - 12x)= 69

6x + 384 - 48x = 69

42x = 384 - 69

X = 315/42

X = 7.5

Substitute x= 7.5 in equation 2

12x + y = 96

12(7.5) + y = 96

90 + y = 96

Y = 6

Therefore, the price of a drink is $7.5