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Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 3 times as old as Daniel. How old is Daniel now?

 Apr 21, 2020
 #1
avatar+711 
+2

Hi guest!
 

This problem was a bit confusing for me - is "Ben and Daniel first met two years ago." extraneous information? It seems like it to me...

 

Well anyways, let's start.

We know that

\(B=20+D\) (since Ben is 20 years older than Daniel)

\(B-3=3D-3\) (since 3 years ago, Ben was thrice Daniel's age)

 

Now all we have to do it plug it in. 

 

\(B=20+D\)

\(B=3D\)

 

\(20+D=3D\)

\(D=10\)

 

\(D+3= \text{his age now}\)

Daniel is now 13.

 Apr 21, 2020
 #2
avatar+25994 
+2

B = 20 + D

B-3 = 3(D-3)         or   -B + 3 = -3D+9     add to first equation

 

 

3 = -3D+9 + 20 + D

-26 = -2D                             D = 13  

 Apr 21, 2020

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