Daily Mail Mindbender

[ginger1945]

Probably published April 2018 but cant see how to get answer £50 . (twice as much as?) Would appreciate
enlightenment!
" Five people spend an average of £73 on their weekly rent
between them. Ella's rent is twice as much as Martin's, who
pays £15 more per week than Tomaso pays. If Tomaso's weekly rent is
75 % of the rent Lucille pays per month, how much rent does Kathy pay per week."

[fiction-factory]

I wondered if anyone had found the answer to this please?

[fiction-factory]

Although the wording is as printed in the paper, the lack of clarity regarding what is meant by a month causes problems here, as others have pointed out.

And as others have also pointe dout, there seem to be too few 'equations' for the number of unknowns although maybe the fact that answers have to be an exact number of pence means some combinations can be ruled out.

A further query I have relates to the opening sentence " Five people spend an average of £73 on their weekly rent between them.". The words "between them" seems odd- does it mean each or in total (and if 'in total' why use the word average?)

[nescio]

if you base everything around Lucille's payment (L), then the overall amount comes to 13L + K = 320.
Trying different values for L eventually gives you
L=23
K=21
M=84
T=69
E=168
This is consistent with all conditions given.

[fiction-factory]

I think that assumes 4 weeks in a month

[fiction-factory]

On the same basis as yours I also found around 700 more solutions- eg
E 138
L 18
m 69
T 54
K 86

[fiction-factory]

Another 'whole pounds' solution based on the 4 weeks in a month assumption is:
E 132.00
L 17.00
M 66.00
T 51.00
K 99.00

[fiction-factory]

I actually have 962 solutions (assuming all values are positive!) if solutions have to be a whole number of pennies.
.
E 177.00
L 24.50
M 88.50
T 73.50
K 1.50

None of these 962 solutions though involves the 'answer' that the OP gave as £50 for Kathy.

[fiction-factory]

If instead we assume there are 4.3333333333.... weeks in a month (52/12) then there are fewer, but still plenty, of solution involving just whole pennies but I can see only one that involves whole numbers of pounds:
E £134
L £16
M £67
T £52
K £96
Average (mean)=£73

But that assumption can be challenged as there are not exactly 52 weeks in a year (there are 52 + 1/7, or 52+2/7 in a leap year).

The question still seems flawed to me.

[fiction-factory]

Are you still around, ginger1945?

[BMicky]

The problem is the question setter has not included a comparison between K's weekly rent and the weekly rent of any of the others. This means that a solution cannot be found using algebra alone. A combination of algebra and trial and improvement can be used but this method will produce several valid answers. I believe there to be an error in the question. Whichever way you work it out the answer cannot be £50.

[fiction-factory]

I think there is a typo- the reference to per month for Lucille should say per week
The key here is Tom who has to pay £15 more than Martin and 75% of Lucille. The only combination that allows this is if Tom pays £50.625p per week (assumes half penny is allowed)

Ella 131.25
Lucille 67.50
Martin 65.625
Tom 50.625
Kathy 50.00

[BMicky]

Quite possible fiction-factory, and your solution does work. I have to say however that the Daily Mail mindbender is rarely so complicated. I think it more likely that the answer of £50 given is incorrect. In my opinion, the most likely of the possible answers to be correct using algebra and trial and improvement is as follows:
L = £20
T = £60
M = £75
E = £150
K = £60
Total = £365
Mean = £73
This of course, is only one of many possible answers. If the question setter had included either, a comparison between K's rent and the rent of one of the others, or two different comparisons between any of the others and one other person, then a definitive solution could be found using algebra alone.
I have come across errors in the Daily Mail Mindbender before and was sad enough to email them once. I received a very nice reply confirming that there was indeed an error. No one is infallible I suppose.