Question

Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.(1 point)
Responses

120x−7=150x−9
120
𝑥
−
7
=
150
𝑥
−
9
; x=15
𝑥
=
15

120 x minus 7 equals 150 x minus 9 ; x equals 15

120+7x=150+9x
120
+
7
𝑥
=
150
+
9
𝑥
; x=−15
𝑥
=
−
15

120 plus 7 x equals 150 plus 9 x ; x equals negative 15

120−7x=150−9x
120
−
7
𝑥
=
150
−
9
𝑥
; x=15
𝑥
=
15

120 minus 7 x equals 150 minus 9 x ; x equals 15

120−7x=150−9x
120
−
7
𝑥
=
150
−
9
𝑥
; x=10

Answer 1

Let x = hours. Remaining amounts: A = 120 − 7x, B = 150 − 9x. Set equal:
120 − 7x = 150 − 9x
Add 9x: 120 + 2x = 150
Subtract 120: 2x = 30
x = 15 hours.

After 15 hours each machine has 15 gallons left.