Donate to Remove ads

Got a credit card? use our Credit Card & Finance Calculators

Thanks to Anonymous,bruncher,niord,gvonge,Shelford, for Donating to support the site

Bicycles

cinelli
Lemon Slice
Posts: 566
Joined: November 9th, 2016, 11:33 am
Has thanked: 242 times
Been thanked: 165 times

Bicycles

#661688

Postby cinelli » April 27th, 2024, 4:50 pm

Bob decided to sell some of his bicycles so went to his local car boot sale and priced his bikes as follows, and he determined not to accept anything below the asking price:

Boardman         £860
Brompton £425
Mercian £425
Harry Quinn £399
Claud Butler £165
Dawes £140
Raleigh £132
Moulton £124
Hercules £68
Falcon £53

In the day he did very well and only one bike remained unsold. Moreover the amount of money he collected in the afternoon was precisely twice the amount collected in the morning. Which bike was not sold and which bikes were sold in the morning and which in the afternoon?

Cinelli

UncleEbenezer
The full Lemon
Posts: 10908
Joined: November 4th, 2016, 8:17 pm
Has thanked: 1485 times
Been thanked: 3030 times

Re: Bicycles

#661692

Postby UncleEbenezer » April 27th, 2024, 6:08 pm

Adding them up, M(orning) + A(fternoon) + U(nsold) = 2791

Since A=2M, that's 3M+U = 2791. Or M = (2791-U) / 3 . Which tells us U has remainder 1 when divided by 3. Only 124 fits. So U = 124, M = 889, A = 1778.

One more constraint: the two 425s can't be split up, or the problem as stated has no unique solution.

By simple inspection, you can't make 889 including either 860 or 2*425. So the most expensive three must be in A.

860 + 2*425 = 1710 = A - 68. So we have M=53+132+140+165+399, A=68+425+425+860.


I hope drinks are on Bob, with all that money!

cinelli
Lemon Slice
Posts: 566
Joined: November 9th, 2016, 11:33 am
Has thanked: 242 times
Been thanked: 165 times

Re: Bicycles

#662490

Postby cinelli » May 2nd, 2024, 7:57 pm

Reply to solution.

This is a model answer. That the two £425 sums can't be split is a nice touch and one that I hadn't considered.

Cinelli

GoSeigen
Lemon Quarter
Posts: 4488
Joined: November 8th, 2016, 11:14 pm
Has thanked: 1628 times
Been thanked: 1627 times

Re: Bicycles

#662576

Postby GoSeigen » May 3rd, 2024, 10:19 am

Sorry Johnny come lately.



If y is the unsold bike, then 3x+y=2791 (total of all prices) . Unsold bike must divisible by 3 with rem 1 the only one is the Moulton.

(2791 - 124)/3 = £889 sold in the morning, £1778 in the afternoon.

-The boardman couldn't sell in the morning, remaining takings would be only £39.
-Checking whether the same argument applies for the boardman, brompton and mercian in the afternoon, 1778-(860+425+425)=68 so by inspection these three bikes and the Hercules sold in the afternoon, the remainder in the morning.



GS
P.S. I thought the Raleigh was the unsold bike as it was massively overpriced but apparently not.

88V8
Lemon Half
Posts: 5914
Joined: November 4th, 2016, 11:22 am
Has thanked: 4268 times
Been thanked: 2633 times

Re: Bicycles

#662653

Postby 88V8 » May 3rd, 2024, 2:35 pm

UncleEbenezer wrote:Adding them up, M(orning) + A(fternoon) + U(nsold) = 2791

Since A=2M, that's 3M+U = 2791. Or M = (2791-U) / 3 . Which tells us U has remainder 1 when divided by 3. Only 124 fits. So U = 124, M = 889, A = 1778.

I wondered who was designing those illegible pastel-on-pastel websites :evil:

V8

servodude
Lemon Half
Posts: 8524
Joined: November 8th, 2016, 5:56 am
Has thanked: 4526 times
Been thanked: 3662 times

Re: Bicycles

#662740

Postby servodude » May 4th, 2024, 6:29 am

GoSeigen wrote:
GS
P.S. I thought the Raleigh was the unsold bike as it was massively overpriced but apparently not.


I wondered if Bob had any more Moultons he wanted rid of?

UncleEbenezer
The full Lemon
Posts: 10908
Joined: November 4th, 2016, 8:17 pm
Has thanked: 1485 times
Been thanked: 3030 times

Re: Bicycles

#662742

Postby UncleEbenezer » May 4th, 2024, 7:26 am

servodude wrote:
GoSeigen wrote:
GS
P.S. I thought the Raleigh was the unsold bike as it was massively overpriced but apparently not.


I wondered if Bob had any more Moultons he wanted rid of?


Many years ago when I did regular CTC club rides on a sunday, we had a member who came on a Moulton. A strange and wondrous beast it was, and from memory, much admired by other club members.

servodude
Lemon Half
Posts: 8524
Joined: November 8th, 2016, 5:56 am
Has thanked: 4526 times
Been thanked: 3662 times

Re: Bicycles

#662749

Postby servodude » May 4th, 2024, 9:22 am

UncleEbenezer wrote:
servodude wrote:
I wondered if Bob had any more Moultons he wanted rid of?


Many years ago when I did regular CTC club rides on a sunday, we had a member who came on a Moulton. A strange and wondrous beast it was, and from memory, much admired by other club members.


The space frame is just a glorious design
even the F looks delightfully retro these dates

cinelli
Lemon Slice
Posts: 566
Joined: November 9th, 2016, 11:33 am
Has thanked: 242 times
Been thanked: 165 times

Re: Bicycles

#662772

Postby cinelli » May 4th, 2024, 10:51 am

Please bear in mind that they were all second hand and some in pretty bad shape. :)

Cinelli

jfgw
Lemon Quarter
Posts: 2586
Joined: November 4th, 2016, 3:36 pm
Has thanked: 1117 times
Been thanked: 1177 times

Re: Bicycles

#662778

Postby jfgw » May 4th, 2024, 11:10 am

UncleEbenezer wrote:Many years ago when I did regular CTC club rides on a sunday, we had a member who came on a Moulton. A strange and wondrous beast it was, and from memory, much admired by other club members.


But what was the bike like?


Julian F. G. W.

servodude
Lemon Half
Posts: 8524
Joined: November 8th, 2016, 5:56 am
Has thanked: 4526 times
Been thanked: 3662 times

Re: Bicycles

#662785

Postby servodude » May 4th, 2024, 11:25 am

jfgw wrote:
UncleEbenezer wrote:Many years ago when I did regular CTC club rides on a sunday, we had a member who came on a Moulton. A strange and wondrous beast it was, and from memory, much admired by other club members.


But what was the bike like?


Julian F. G. W.


Sticky??


Return to “Games, Puzzles and Riddles”

Who is online

Users browsing this forum: No registered users and 5 guests