Let's call the number of pages we have read [tex]m[/tex]. To find the number of pages we have left to read, we'll need to subtract the number of pages we've read from the total number of pages in the book. Our total page count is 193, and the number of pages we've read is the unknown [tex]m[/tex], so the number of pages we haven't read can be written as [tex]193-m[/tex]. With that knowledge, let's construct the rest of our equation.
"He has read three pages more than one-fourth of the number of pages he hasn't yet read." The first key phrase here is "he has read." What this means is that the number of pages he's read, which we've named [tex]m[/tex], is equal to everything in the rest of the sentence. "Thee pages more than" means that we're going to be adding 3 to whatever the next quantity described is, which, in this case, is "one-fourth of the number of pages he hasn't yet read." We already established earlier that "the number of pages he hasn't yet read" is [tex]193-m[/tex], so one-fourth of that would be [tex] \frac{1}{4} (193-m)[/tex]. Putting everything together, we get the following equation:
[tex]m= \frac{1}{4} (193-m)+3[/tex]
To solve for [tex]m[/tex], we might first want to eliminate the fraction 1/4 by multiplying both sides of the equation by 4, obtaining
[tex]4m=193-m+12[/tex]
Solving for m, we get:
[tex]4m=193+12-m\\5m=205\\m=41[/tex]
Now that we have m, it's a simple matter to solve for [tex]193-m[/tex]:
[tex]193-41=152[/tex]
So, he has not yet read 152 pages.
