Two vats are being filled by two different pumps. The first vat has 10 gallons is being filled at a rate of 12 gallons per second. The second vat has 25 gallons and is being filled at a rate of 10 gallons per second. After how many seconds will both vats have the same amount of liquid?

Answer 1

Let t be the number of seconds that have passed.
The amount of liquid in the first vat is 10 + 12t.
The amount of liquid in the second vat is 25 + 10t.
10 + 12t = 25 + 10t
2t = 15
t = 7.5
After 7.5 seconds, both vats will have the same amount of liquid. Answer: \boxed{7.5}.

Answer 2

A movie theater offers a special pricing for membership. The normal cost is $7.50 per ticket. The membership costs $5 per ticket but an initial fee of $25. After how many tickets are both options the same price?