MHB How Many Books Did Devi Read in a Month?

[Johnx1]

Tom and Devi read 34 books in a month. Devi and Weiming read 58 books in the same month. Weiming read twice as many books as Tom. How many books did Devi read in that month?

My way of answering it:

x + x + 2x = 92

x = 23

I got stuck there.However
The book answer is 58 - 34. Then 34 -24 = 10. So Devi read 10 books, But I'm not sure how they got that answer.

 

[Evgeny.Makarov]

x + x + 2x = 92

This would be correct if Tom and Devi read the same number of books, which is denoted by $x$ in your equation. But there is no reason to think so.

Let $t$, $d$ amd $w$ be the number of books read by Tom, Devi and Weiming, respectively. Then we can get the following equations from the problem statement.
\[
\left\{
\begin{aligned}
t+d&=34\\
d+w&=58\\
w&=2t
\end{aligned}
\right.
\]
Substituting $w$ from the third equation into the second one, we get
\[
\left\{
\begin{aligned}
t+d&=34\\
2t+d&=58\\
\end{aligned}
\right.
\]
The difference between the left-hand sides, i.e., $(2t+d)-(t+d)=t$, and from the right-hand sides the same difference is $58-34=24$. Therefore, $t=34$. Then from the first equation we get $d=34-t=34-24=10$.

 

[Greg]

Though it's good to work it out as Evgeny did there is a shortcut:

T + D = 34

2T + 2D = 68
2T + D = 58
---------------------
0 + D = 10