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x = ship.age y = boiler.age

we know that: x + y = 42 and x = 2(y-x) => y = x/2 + x

since x + y = 42 and y = x/2 + x => x + (x + x/2) = 42 => 2x + x/2 = 42 => x/2 = 42-2x => x = 2(42-2x) => x = 84 - 4x => x+4x = 84 => x = 84/5 = 16.8

since y = x/2 + x y = 16.8/2 + 16.8 y = 8.4 + 16.8 y = 25.2

To prove that this is correct: x+y = 16.8 + 25.2 = 42.0

schalla- May 29, 2008

Article Rating 3 out of 5

Itzik, thanks for the puzzles - they're great, though I often give up before applying much thought to them!

schalla, I can't say I stepped through all of your algebra, but I can tell that your answer is not correct. You are saying that x(ship age)=16.8, and y(boiler age)=25.2, right? Assuming that, what you calculated would be the following: The ship is twice as old as the ship was when the boiler was the age that the ship is now. Another part that shows it is not correct is that the ship must be older than the boiler, since it was once the current age of the boiler.

I think I figured out the answers are x=24, y=18, but I didn't get all the way there with algebra, so that wouldn't really count... We know 42=x+y We know that x=2*(y-(x-y)) (that's twice of (the boiler age minus their difference)) Solve for y in terms of x: x=2*(y-(x-y)) x/2=y-(x-y) (x/2)+(x-y)=y x/2+x=y+y x/2+x=2y (x/2+x)/2=y y=((x/2)+x)/2 replace y with expression of x: Therefore 42=x+(((x/2)+x)/2) Here's where we should theoretically be able to solve for x, but I couln't figure it out with the nested expressions, so I used Excel for trial & error calculation: Name a cell x; enter this formula in another cell:=x+(((x/2)+x)/2); enter whole numbers so get close to 42, and discover that 24 makes it come out to 42. Then I solved for y with some fuzzy algebra and late-night logic: 24/2=12, and I know that y has to be half way between x and x/2, so half of the difference is (24-12)/2=6, and x-{half the difference} is 24-6, or 18. To check: 24(ship)+18(boiler)=42, and when the ship was 18, the boiler was 12, which is half of the current age of the ship (24). I look forward to seeing what I missed: how to exactly solve for the values given 42 as the sum.

Dan W- May 30, 2008

Article Rating 4 out of 5

I was counting on new lines without a blank line, so I appologize for the run-together formatting... Many of the spaces were meant to be line breaks.

Dan W- May 31, 2008

Article Rating 4 out of 5

Dan W:

My answer is the same as yours, following similar logic until the end.

If I jump down in your explanation to where you have:

x = 2*(y-(x-y))

I think this is the point to simplify before solving:

x = 2 * (2y - x)

x = 4y - 2x

3x = 4y

(3x)/4 = y

Now, we can substitute for y in the original known equation:

x + (3x)/4 = 42

Combine with common denominators:

(4x)/4 + (3x)/4 = 42

(7x)/4 = 42

x = 24

y = 42 - x

y = 18

jeffem- June 01, 2008

Article Rating 4 out of 5

Thanks, jeffem! I had forgotten how to simplify x=2*(y-(x-y)) and combine with common denominators.

Dan W- June 02, 2008

Article Rating 4 out of 5

Nice one. I messed up this piece x=2*(y-(x-y)) :(

schalla- June 05, 2008

Article Rating 5 out of 5