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)
Let x represent the number of days it will take for the two machines to have the same amount of ice cream left.
After x days, the vanilla ice cream machine will have 180 - 20x cups of ice cream left.
After x days, the chocolate ice cream machine will have 140 - 16x cups of ice cream left.
Setting the two expressions equal to each other, we have:
180 - 20x = 140 - 16x
Now, let's solve for x:
180 - 140 = -16x + 20x
40 = 4x
x = 10
Therefore, it will take 10 days for the two machines to have the same amount of ice cream left.
Let's assume the number of days it takes for the vanilla ice cream machine to have the same amount of ice cream left as the chocolate ice cream machine is represented by the variable 'x'.
The vanilla ice cream machine starts with a capacity of 180 cups and sells 20 cups per day, so the amount of ice cream left after 'x' days is 180 - 20x.
Similarly, the chocolate ice cream machine starts with a capacity of 140 cups and sells 16 cups per day, so the amount of ice cream left after 'x' days is 140 - 16x.
To find when the two machines will have the same amount of ice cream left, we can set these two expressions equal to each other and solve for 'x':
180 - 20x = 140 - 16x
To solve this equation, we can first simplify it:
20x - 16x = 180 - 140
4x = 40
Dividing both sides of the equation by 4:
x = 10
Therefore, it will take 10 days for the vanilla ice cream machine and the chocolate ice cream machine to have the same amount of ice cream left.