Answer:
p = t * 12.5
Step-by-step explanation:
To find the relationship between hours of work and the pay, I divided the total paycheck given by the 25 hours of work, which got me what a 25th of that paycheck would be, which represents what you would earn in an hour with a flat rate.
312.50 / 25 = 12.5
Check:
12.5 * 25 (hours of work) = 312.50 (Given total paycheck)
That's how we know the pay per hour, which is the relationship between t and p.
Set it up like a regular equation. I used:

As you can see, however, I inserted the "less than" symbol rather than the equal sign because values greater than a certain value can also equal "x". Solve it like a normal equation and you will arrive at:
<u>
</u>

This means that, as long as x is greater than 45, "6x" will be greater than "3x+135". Thus, if you bring 46 students, the Science Center will cost less.