Problem Solving

VJesus12 wrote: ↑

Sun Apr 25, 2021 2:09 pm

In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?

(A) 15
(B) 16
(C) 25
(D) 40
(E) 46


Answer: B

Source: Official Guide

Let's start with a word equation

We can write: (total number of pages to be read at INTENDED rate of 90 pages/day) = (total number of pages ACTUALLY read at 75 pages/day) + 690 more pages

Let x = number of days to complete reading assignment at 90 pages per day
So, x - 6 = number of days reading at 75 pages per day (since Terry spent the last 6 days reading 690 pages)

At a rate of 90 pages/day, 90x = number of pages that COULD be read in x days
At a rate of 75 pages/day, 75(x - 6) = number of pages ACTUALLY read in x-6 days

We get: 90x = 75(x - 6) + 690
Expand to get: 90x = 75x - 450 + 690
Simplify to get: 90x = 75x + 240
We get: 15x = 240
Solve: x = 240/15 = 16

Answer: B

Cheers,
Brent