Question

An ice cream shop makes vanilla and chocolate ice cream. The vanilla ice cream machine has a 180-cup capacity, and it sells 20 cups per day. The chocolate ice cream machine has a 140-cup capacity, and it sells 16 cups per day. Write and solve an equation to show when the two machines will have the same amount of ice cream left.(1 point)
Responses

180+16x=140+20x
180
+
16
𝑥
=
140
+
20
𝑥
; x=−10
𝑥
=
−
10

180 plus 16 x equals 140 plus 20 x ; x equals negative 10

180−20x=140−16x
180
−
20
𝑥
=
140
−
16
𝑥
; x=20
𝑥
=
20

180 minus 20 x equals 140 minus 16 x ; x equals 20

180−20x=140−16x
180
−
20
𝑥
=
140
−
16
𝑥
; x=10
𝑥
=
10

180 minus 20 x equals 140 minus 16 x ; x equals 10

140+16x=180+20x
140
+
16
𝑥
=
180
+
20
𝑥
; x=10

Answer 1

Set amounts after x days equal. Vanilla: 180 − 20x. Chocolate: 140 − 16x.

Equation: 180 − 20x = 140 − 16x
Solve: 180 − 140 = 20x − 16x → 40 = 4x → x = 10.

So x = 10 days. (Check: 180 − 20·10 = −20 and 140 − 16·10 = −20, so algebraically they match at 10 days.)