HELP - I FORGOT ALGEBRA

If you wish to formally set it up, you could write two equations with two unknowns. In this case, we do not know how many pages per day he was reading (I will call this rate r), and we don't know how many days it took him to read the book (I will call this d).

Using dimensional analysis we know that

total # of pages * # of days per page = # of days spent

(pgs) * (days/pg) = (days)

\(480 * \frac{1}{pgs/day} = d\)

\(480 * \frac{1}{r} = d\)

Similarly, we can write a second equation for the additional piece of given information (that we could have finished 5 days sooner reading at a rate of 16 more pages a day).

\(480 * \frac{1}{(r+16)} = d-5\)

Now we have two equations with two unknowns. I would solve one of the two for r and then substitute into the other equation for r. This will give you a single equation that you can solve for d, the desired quantity.

In this case the final equation is a quadratic that can be factored to yield two solutions, one of which is negative and thus can be ignored (it didn't take him negative days to complete the book).

\((d-15)(d+10) = 0\)

Hence d must be 15.

As you can see, this process is likely more time consuming than using the multiple choices to work backwards.