Question

On the first day Louis read half of the book, on the second day he read 3/8 more and 40 pages remain. How may pages where their in the book?

Answer 1

Pleae, note that, your problem is a mathematization problem. I think that If I call n, the number of pages of your book, we can write:
\[\frac{ n }{ 2 }+\frac{ 3 }{ 8 }n+40=n\]
because on the first day Louis read n/2 pages, on the secon day, Louis read (3/8)*n more and 40 pages reamain, so the sum below:
n/2 + (3/8)*n+40,
must be equal to n.
Please try to solve the above equation in order to find the value of n

Answer 2

what is the answer?

Answer 3

Sorry, but by the code of conduct, I can not tell you the answer directly!

Answer 4

how to get the answer? please help me. i need it right now

Answer 5

you have to solve the above equation for n, in order to that, you can calculate the least common multiple. Do you know what is the least common multiple among 1, 8 and 2?

Answer 6

no

Answer 7

do you know the rule to apply to calculate the least common multiple?

Answer 8

no

Answer 9

I think its 16

Answer 10

ok! now I write the subsequent factorizations:
1=1
2=1*2,
8=2*2*2=2^3
please note that in order to find the least common multiple (LCM) you have to pick common factors with highest exponent, and all not common factors with highest exponent, so?

Answer 11

16

Answer 12

Sorry, what is the highest exponent of 2?

Answer 13

3

Answer 14

so, LCM=...

Answer 15

8

Answer 16

that's right!

Answer 17

what will i do next?

Answer 18

I write. Next step you have to multiply both sides of the equation that I wrote, by 8, please write what you get

Answer 19

what is the answer i will try to figure out?

Answer 20

for example the left side becoes this:
\[8*\frac{ n }{ 2 }+8*\frac{ 3 }{ 8 }n+8*40=\]
\[=4*n+3*n+320=\]
\[=7*n+320\]
now, do the same with the right side, please!

Answer 21

n=320

Answer 22

that's right, nevertheless I ask you, what is the right side of the equation?

Answer 23

8n

Answer 24

so waht is the answer?

Answer 25

that's right, so we have to solve the subsequent equation:
\[7*n+320=8*n\]
now, in order to that, please add (-7*n) to both sides of that last equation

Answer 26

n=320

Answer 27

then? what will i do next how will i know the pages of the book?

Answer 28

ok!we have:
n=20, so the book of Louis has 320 pages!

Answer 29

sorry n=320....

Answer 30

thank you

Answer 31

how to check the answer?

Answer 32

by the correctness of our reasoning

Answer 33

how?

Answer 34

I think that our reasoning is correct, so our answer is right, that's all!
you have to trust of your reasoning!

Answer 35

ok btw, Thanks again,

Answer 36

thank you!