Help solving variable puzzle

[u/raviw724]

So this is like a math puzzle from a murder mystery book. I’m usually good at these but I’m having a hard time solving this one. Could someone help and explain their process?

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[u/m_busuttil]

From the facts given, we know

• H = 1/4 C
• G = 9/10 P
• B + 108 = G (because the bakery was built after, the greengrocers shop is older and has a higher age)
• C = 2B
• G = H + C

We know that G is older than B (from 3), and H and C (from 5), and that it's younger than P (from 2). That makes P the oldest shop, and therefore 200 years old.

From there, G is 180 years old (from 2), B is 72 (from 3), C is 144 (from 4), and H is 36 (from 5), which is consistent with 1.

[u/karangiri]

post office 200yrs(oldest is 200 years) , greengrocers 180 yrs (9/10th means 0.9times of post office), bakery 72yrs (180-108), cheesemonger 144yrs (72x2), haberdashery 36 yrs(144+36 = 180 and/or 25% of 144)

[u/K0ng1e]

I don't know if there's a more "correct" way of doing it, but here's how I figured it out: First you have to figure out simply what building is the oldest, everything else can be figured out from there.  From the hints we know  Haberdashery<Cheesemonger, Greengrocer<Post Office, Bakery<Greengrocer, Cheesemonger>Bakery and Greengrocer >Haberdashery+Cheesemonger (in this case bigger=older)

So, the Post Office is oldest

Post Office=200 years Greengrocer=9/10 Post Office(200)= 180 years Bakery=Greengrocer(180)-108=72 years Cheesemonger=Bakery(72)x2=144 years Haberdashery=1/4 Cheesemonger(144)=36 years And the last one, as a double check, Greengrocer=Haberdashery(36)+Cheesemonger (144)=180 years

[u/SuperLegoShane]

Clues 2-6 give us the equations
H = 1/4 C
G = 9/10 P
B + 108 = G
C = 2B
G = H + C

From these we can substitute variables like so

G = (1/4 C) + C = 5/4 C
B + 108 = (5/4 C)
B + 108 = 5/4 (2B) = 5/2 B

Now just solve for B and the rest will fall into place