HELP - I FORGOT ALGEBRA

Question

I can set up the equation for GMAT CLUB TEST 15 problem 20 but cannot seem to solve. Is there anyone that can break this down for me? I am banging my head up against the wall in frustration. (see below).

Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?

10
12
15
16
18

Any help is much appreciated!

trunksli · Answer

I would work backwards.

1) You are given number of days, so divide 480 by one of the choices to get the number of pages read per day. 
2) Add 16 to that. 
3) Divide 480 by that total, see if that gets to the 5 less than number of days you used.

brau0300 · Answer

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.

ingoditrust · Answer

My method is a little time intensive:

let n be the days taken to read the book initially
now the with increased number of pages being read everyday (+16) days taken = n-5

We can get the number of pages read per day by

number of pages in the book / days taken to read the book  
so with slow speed = 480/n
with fast speed = 480/(n-5)

We also know that the difference between the number of pages per day between the two different speeds is 16

480/(n-5) - 480/n = 16

approach 1 : simplify it make it a quadratic equation and you will get the answer as 15

approach 2 : plug int he values

10 = > (96-48) ! = 16
12 = > 480/7 - 40 != 16 
 15 = > 48 - 32 = 16 <Bingo>  
16
18

whiplash2411 · Answer

This can be solved by setting up two equations concerning the total number of pages.

Let him read p pages per day initially and let it take d days for him to finish reading. So the total number of pages is pd.

pd = 480  (1)

In the other condition stated, it says that he could have finished the book 5 days earlier if he had read 16 more pages per day.

This means that he reads (p+16) pages per day and it takes him (d-5) days to finish the book. The total number of pages in this case is (p+16)(d-5).

But note that this is the same as the total number of pages hasn't changed.

(p+16)(d-5) = 480

Expanding this we get:  pd - 5p + 16d - 80 = 480  (2)

Substituting (1) into (2) in place of pd, we get:

480 - 5p + 16d - 80 = 480

16d - 5p = 80

Now we can substitute  p = \frac{480}{d}  into this equation to get the following quadratic:

16d - \frac{2400}{d} = 80

16d^2 - 80d - 2400 = 0

Dividing by 16 throughout

d^2 - 5d - 150 = 0

d^2 - 15d + 10d - 150 = 0

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

d = 15  or  -10

But d, being the number of days, cannot be negative. Hence d = 15 is the answer. Answer choice C.

Hope this helps.

mustdoit · Answer

Better work with choices....

E is out straightaway because 480/18 is not an integer....Tom can not read pages in fractions....

Now With choices...

A

480/10 = 48 pages add 16 pages 64 480/64 doesnt gives 5 days (not an integer)

B

480/12 = 40 pages add 16 pages 56 480/56 doesnt gives 7 days (not an integer)

C

480/15 = 32 pages add 16 pages 48 gives 480/48 as 10 days......Answer...

No need to check D

Hope this helps ......( I would better avoid forming equations in this case)

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