Answer:
The system of equations are
x+y=557
![\frac35x+\frac56 y=407](https://tex.z-dn.net/?f=%5Cfrac35x%2B%5Cfrac56%20y%3D407)
The total pages in shorter book is 245
The total pages in longer book is 312
Step-by-step explanation:
Given that,
Scott has read 407 of the total number of 557 pages, which
of the shorter book and
of longer book.
Total number of pages of shorter book be x and longer book be y.
Then,
page of the shorter book ![=\frac35 x](https://tex.z-dn.net/?f=%3D%5Cfrac35%20x)
pages of the longer book = ![\frac56y](https://tex.z-dn.net/?f=%5Cfrac56y)
So, he has read ![=\frac35x+\frac 56y](https://tex.z-dn.net/?f=%3D%5Cfrac35x%2B%5Cfrac%2056y)
Total number of pages of both book is = x+y
According to the problem,
x+y=557.........(1)
.......(2)
We can write equation (2) as
![\frac35x+\frac56 y=407](https://tex.z-dn.net/?f=%5Cfrac35x%2B%5Cfrac56%20y%3D407)
![\Rightarrow \frac{18x+25y}{30}=407](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B18x%2B25y%7D%7B30%7D%3D407)
![\Rightarrow {18x+25y}=407\times 30](https://tex.z-dn.net/?f=%5CRightarrow%20%7B18x%2B25y%7D%3D407%5Ctimes%2030)
......(3)
Now 18 times of equation (1) subtract from equation (3)
18x+25y=12210
18x+18y=10026
- - -
_______________
25y-18y=12,210-10,026
⇒7y=2,184
![\Rightarrow y=\frac{2184}{7}](https://tex.z-dn.net/?f=%5CRightarrow%20y%3D%5Cfrac%7B2184%7D%7B7%7D)
⇒y= 312
Plug y=312 in equation (1)
x+312=557
⇒x=557-312
⇒x=245
The total pages in shorter book is 245
The total pages in longer book is 312