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# help

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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
+711
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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
+25994
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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