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 an equation to show when the two machines will have the same amount of ice cream left
To find out when the two machines will have the same amount of ice cream left, we need to set up an equation based on the information given.
Let's denote the number of days as "d".
For the vanilla ice cream machine, the number of cups remaining can be calculated using the formula:
CupsRemainingVanilla = CapacityVanilla - (Number of cups sold per day * Number of days)
CupsRemainingVanilla = 180 - (20 * d)
For the chocolate ice cream machine, the number of cups remaining can be calculated using the formula:
CupsRemainingChocolate = CapacityChocolate - (Number of cups sold per day * Number of days)
CupsRemainingChocolate = 140 - (16 * d)
When the two machines will have the same amount of ice cream left, the number of cups remaining for vanilla will be equal to the number of cups remaining for chocolate. So we can set up the equation:
CupsRemainingVanilla = CupsRemainingChocolate
180 - (20 * d) = 140 - (16 * d)
Simplifying the equation, we get:
180 - 20d = 140 - 16d
Now we can solve this equation for "d" to find the number of days when both machines will have the same amount of ice cream left.
Let's start by defining the variables:
v = Vanilla ice cream cups remaining
c = Chocolate ice cream cups remaining
d = Number of days elapsed
We'll assume both machines start with their full capacity. Now let's create equations based on the given information:
For the vanilla ice cream machine:
v = 180 - 20d
For the chocolate ice cream machine:
c = 140 - 16d
To find when the two machines will have the same amount of ice cream left, we need to set v equal to c and solve for d:
180 - 20d = 140 - 16d
Now let's simplify the equation:
-20d + 16d = 140 - 180
Combine like terms:
-4d = -40
To solve for d, divide both sides of the equation by -4:
d = -40 / -4 = 10
Therefore, the two machines will have the same amount of ice cream left after 10 days.
Let's assume that the number of days it takes for the two machines to have the same amount of ice cream left is "d".
The amount of vanilla ice cream left after "d" days can be calculated as:
180 - 20d
Similarly, the amount of chocolate ice cream left after "d" days can be calculated as:
140 - 16d
To find the point at which the two machines have the same amount of ice cream left, we can set these two expressions equal to each other:
180 - 20d = 140 - 16d
Simplifying this equation, we get:
4d = 40
Dividing both sides by 4, we get:
d = 10
Therefore, it will take 10 days for the two machines to have the same amount of ice cream left.