Respuesta :
Answer:
The system of equations are
x+y=557
[tex]\frac35x+\frac56 y=407[/tex]
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 [tex]\frac35[/tex] of the shorter book and [tex]\frac56[/tex] of longer book.
Total number of pages of shorter book be x and longer book be y.
Then,
[tex]\frac35[/tex] page of the shorter book  [tex]=\frac35 x[/tex]
[tex]\frac56[/tex] pages of the longer book = [tex]\frac56y[/tex]
So, he has read [tex]=\frac35x+\frac 56y[/tex]
Total number of pages of both book is = x+y
According to the problem,
x+y=557.........(1)
[tex]\frac35x+\frac56 y=407[/tex].......(2)
We can write equation (2) as
[tex]\frac35x+\frac56 y=407[/tex]
[tex]\Rightarrow \frac{18x+25y}{30}=407[/tex]
[tex]\Rightarrow {18x+25y}=407\times 30[/tex]
[tex]\Rightarrow {18x+25y}=12,210[/tex]......(3)
Now 18 times of equation (1) subtract from equation (3)
  18x+25y=12210
  18x+18y=10026
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    25y-18y=12,210-10,026
   ⇒7y=2,184
   [tex]\Rightarrow y=\frac{2184}{7}[/tex]
   ⇒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
The system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is
3 / 5 x + 5 / 6 y = 407
x + y = 557
How to model a system of equation?
Scott has read 407 of the total number of 557 pages, which is  3 / 5 of the shorter book and 5 / 6 of longer book.
x = number of pages in the shorter book
y = number of pages in the longer book
Therefore, the system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is as follows;
3 / 5 x + 5 / 6 y = 407
x + y = 557
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