Answer:
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.
