In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pag

M7MBA wrote: ↑

Thu Jan 07, 2021 10:31 am

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

M7MBA wrote: ↑

Thu Jan 07, 2021 10:31 am

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

Solution:

We are given that Terry’s initial plan was to read 90 pages per day for “T” days. We can multiply, getting 90T for the total work that was supposed to be done for the entire reading assignment.

We are next told that she actually started out reading 75 pages per day until she had 6 days left to finish the project. Since T represents the total number of days we can say she read 75 pages per day for (T–6) days. Finally, when we multiply, we see that her work done on the T–6 days was 75T–450.

To finish this problem we need to set up one final equation. We are told that she must read 690 pages in the last 6 days to complete the assignment. Recall that 90T denotes a completed assignment. Thus, we can say:

75T – 450 + 690 = 90T

75T + 240 = 90T

15T = 240

T = 16

Answer: B