Question

Scott is reading two books at the same time to prepare for a report he is writing. So far, he has read 407 of the total number of 557 pages, which is Three-fifths of the shorter book and StartFraction 5 Over 6 EndFraction of the longer book. Which system of equations 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?

Answer 1

Answer:

The system of equations are

x+y=557

$\frac35x+\frac56 y=407$

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 $\frac35$ of the shorter book and $\frac56$ of longer book.

Total number of pages of shorter book be x and longer book be y.

Then,

$\frac35$ page of the shorter book  $=\frac35 x$

$\frac56$ pages of the longer book = $\frac56y$

So, he has read $=\frac35x+\frac 56y$

Total number of pages of both book is = x+y

According to the problem,

x+y=557.........(1)

$\frac35x+\frac56 y=407$.......(2)

We can write equation (2) as

$\frac35x+\frac56 y=407$

$\Rightarrow \frac{18x+25y}{30}=407$

$\Rightarrow {18x+25y}=407\times 30$

$\Rightarrow {18x+25y}=12,210$......(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

     $\Rightarrow y=\frac{2184}{7}$

     ⇒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