Trigonometry is difficult

Question

The pages of a three-volume encyclopedia are numbered consecutively, starting with page one. There are an equal number of pages in each volume. The sum of the numbers on the fifth page of each volume is 1335. How many pages are in each volume?

Answer 1

Wow, what a mouthful!

There are the same number of pages in each volume:

a = b = c

The fifth numbers of each of the volumes add up to 1335:

first volume is 5

second volume is the number of pages from the first volume plus five: a + 5

third volume is the the number of pages from the first and second volume plus five: a + b + 5

so:

5 + a + 5 + a + b + 5 = 1335

but a = b

5 + a + 5 + a + a + 5 = 1335

15 + 3a = 1335

3a = 1320

a = 440

So the number of pages in each volume is 440.

since they are consecutive

Volume a 1-440

Volume b 441-840

Volume c 841-1320