Could you solve Test 6, Section 4, number 18 for me? Thanks!

Sure thing. You’ve got your riser-tread formula: 2hd = 25. Now you’re told that d must be at least 9 and h must be at least 5. Translating that into math: d ≥ 9 and h ≥ 5.

Of course, since 2hd must always equal 25, there are also upper bounds on the values of d and h—they can’t be too small, but they can’t be too big, either. In fact, as one gets bigger, it forces the other one to get smaller.

Let’s plug in 9 for d (that’s its minimum value) and see what we’d get for h:

2hd = 25
2h + 9 = 25
2h = 16
h = 8

What would happen if we plugged 10 in for d instead?

2h + 10 = 25
2h = 15
h = 7.5

Ahh, see? If d gets bigger, it makes h smaller. So the BIGGEST value we can have for h is 8 if we have a minimum value for d at 9.

We now know that h must be at least 5, but also cannot be greater than 8: 5 ≤ h ≤ 8 is the answer.