NY Post Math Problem, Solved
a clear (I hope) explanation
I got two emails asking me about this problem, which is apparently causing a stir online. As I tutor mathematics, the emailers hoped I could provide a clear explanation. Mathematics is not nearly as difficult as most people think, and I hope this post will help demonstrate why.
The problem doesn’t specifically say that Klein started the book on Monday, but in order to solve the problem, we must assume this to be the case.
On Monday, he read the first 30 pages. On Tuesday, he read 1/8 of the book. On Wednesday, he read 1/4 of the book and thus completed it.
That gives us an equation. 30 pages + 1/8 of the book + 1/4 of the book = 1. (As in, one complete, whole book.)
That’s the first thing to understand: 1 is always a fraction of the number of parts we are dealing with, over itself. Think of a pie:
If we cut this pie into four pieces but don’t eat any, we still have one whole pie. Why? Because we have four fourths: 4/4.
So now we have an equation of 30 pages of book + 1/8 of book + 1/4 of book = 1 whole book.
To deal with fractions in an equation, we need a common denominator.
Between eighths (1/8 of the book) and fourths (1/4 of the book), the common denominator available to us is 8. Let’s see if we can use that to figure out what fraction of the book 30 pages would be!
Because we are dealing in eighths, we can turn our 1 on the right hand side (RHS) of the equation into 8/8. And now we can use the rules of algebra, which tell us we can do whatever we want to an equation, as long as we do it to both sides:
So now we know that 30 pages is 5/8 of the total book.
We are asked to find the length of the book.
There are two ways to do this. One we can do in our heads, if we know our times tables.
If 30 is 5/8 of something, then 1/8 of that thing is 30 divided by 5. 30 divided by 5 is 6. If 1/8 of the book is 6 pages, then the full book, 8/8, would be 8 x 6 or 48.
The other way is to make an equation of it, using x as our unknown number of pages, and solve it with the rules of algebra:
Using the rules of algebra, we see that x = 48 pages.
I’ve seen a few other methods of solving it floating around. I hope this one is clear and understandable.
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My old math teachers would be proud, I saw the math problem and before scrolling down managed to figure it out and get the correct answer before I continued reading, guess I remember more of those old algebra lessons then I thought
Good explanation, but also kinda sad that anyone who's gotten past algebra I might have trouble solving it.
Years ago when my youngest son was in 2nd or 3rd grade, he came down with strep throat. Having plenty of time to burn, I took the days off to stay with him. His sister brought home his homework assignments, part of which was math.
So I'm sitting there looking at what the assignment is, thinking to myself "how do you solve this without using algebra?". Coming up with nothing else and not knowing what had been taught in class, I taught my 7 or 8 year old son simple algebra - how to handle simple arithmetic, cross over the bridge and change the sign and all that. He had it figured out in about 30 minutes. Could he have solved THIS word problem? Probably not. But he was 7 or 8, not 14 or 15.