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.
Let's use "v" to represent the amount of vanilla ice cream left and "c" to represent the amount of chocolate ice cream left.
After "d" days, the amount of vanilla ice cream left would be:
v = 180 - 20d
And the amount of chocolate ice cream left would be:
c = 140 - 16d
To find when the two machines have the same amount of ice cream left, we need to set these equations equal to each other and solve for "d":
180 - 20d = 140 - 16d
Subtract 140 from both sides:
40 - 20d = -16d
Add 16d to both sides:
40 = 4d
Divide both sides by 4:
d = 10
Therefore, the two machines will have the same amount of ice cream left after 10 days.