All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
The royal sisters (Posted on 2018-04-09) Difficulty: 2 of 5
the Queen of Ruritania went shopping with her younger sister.
Each bought as many lengths of silk as she is years old and as many yards of each length as she bought lengths and paid for it as many francs per yard as she bought yards of each length.

The Queen spent 5803 francs more than her sister.
How old is the Queen?

Source : The weekend problems book; collected by Hubert Phillips UK 1932

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Analytic solution | Comment 2 of 3 |
Queen age x, bought x lengths of, x yards at x per yard.  Cost = x^3
Likewise sister age y, cost = y^3.

It seems reasonable that x-y=7 so

x^3 - (x-7)^3 = 5803
21x^2 - 147x + 343 = 5803
x^2 - 7x - 260 =0

which is quadratic with positive solution x=20.

Checking: 20^3=8000, 13^3=2197, 8000-2197=5803

Note: putting y=x-7 into (x^2+xy+y^2)=829 yields the same quadratic

  Posted by Jer on 2018-04-10 09:49:36
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information