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

Sure thing. You’ve got your riser-tread formula: 2*h* + *d* = 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 2*h* + *d* 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*:

2*h* + *d* = 25

2*h* + 9 = 25

2*h* = 16

*h* = 8

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

2*h* + 10 = 25

2*h* = 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.