Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling at a rate of 6 gallons per minute. The other is already filled with 10 gallons, and it is continuing to fill at a rate of 4 gallons per minute. Write an equation to show when the two vats will have an equal amount of liquid. Use x as your variable.
Let x be the number of minutes it takes for the two vats to have an equal amount of liquid.
At x minutes, the first vat will have 6x gallons of liquid.
At x minutes, the second vat will have 10 + 4x gallons of liquid.
To find when the two vats have an equal amount of liquid, we set the expressions equal to each other:
6x = 10 + 4x
A yoga studio has two participation plans. For the first plan, the cost is $8 per visit. For the second plan, the cost is $40 per month, and $2 per visit. Wrote an equation to show the number of visits per month that it would take for the two plans to be equal. Use x as your variable.
Let x be the number of visits per month.
For the first plan, the cost is simply $8 per visit. So the total cost is 8x.
For the second plan, the cost is $40 per month plus $2 per visit. So the total cost is 40 + 2x.
To find when the two plans have an equal cost, we set the expressions equal to each other:
8x = 40 + 2x
A diner makes vanilla milkshakes and chocolate milkshakes. The vanilla milkshake machine has a 300-cup capacity, and sells 15 cups per day. The chocolate milkshake machine has a 280-cup capacity and sells 20 cups per day. Write an equation to show when the two machines will have the same amount of milkshake left. Use c as your variable.
Let c be the number of cups of milkshake left.
For the vanilla milkshake machine, the initial number of cups is 300 and it sells 15 cups per day. So the number of cups left after d days is 300 - 15d.
For the chocolate milkshake machine, the initial number of cups is 280 and it sells 20 cups per day. So the number of cups left after d days is 280 - 20d.
To find when the two machines will have the same amount of milkshake left, we set the expressions equal to each other:
300 - 15d = 280 - 20d
My bad I meant make the variable x so the answer is 300-15x=280-20x
No problem! I apologize for the confusion.
Let x be the number of days.
For the vanilla milkshake machine, the initial number of cups is 300 and it sells 15 cups per day. So the number of cups left after x days is 300 - 15x.
For the chocolate milkshake machine, the initial number of cups is 280 and it sells 20 cups per day. So the number of cups left after x days is 280 - 20x.
To find when the two machines will have the same amount of milkshake left, we set the expressions equal to each other:
300 - 15x = 280 - 20x