11 Plus Exams Forum

Please can someone help with this problem question

The money in Tim's wallet consists entirely of 2p and 5p coins. Sam asked him if he could change a £1 coin, but he was not able to do it exactly. What is the greatest amount of money that Tim could have in his wallet?

DD insists it is £1.04. Answer in booklet is £1.03.

DD's explanation:

99p is where she stopped using 2p and 5 p coins. But since the question asked for greatest amount, DD added another 5p coin to make £1.04.

DD said that this way, even though Tim has £1.04, he still cannot give Sam change of £1 exactly, but can only manage 99p, with the extra 5p coin hindering his (Tim's) objective of wanting to give Sam the exact change.

I am completely lost myself, as I had thought the answer was 99p.

if you had £1.04 you would have 2x2p somewhere so you could give change for £1.

99p = 19x 5p (say) + 4p

add another 5p and you can give the 20 5p coins.

Clearly 20 x 5p gives £1

But 19 x 5 gives a nice odd number... 95p

Bearing in mind 18 x 5 = 90p and we have 19 5ps so having 5x 2p would also bring us to £1; we must therefore have less than 5 2ps otherwise we would have reached £1 via the 18 x 5p route.

Therefore 19 x 5 + 4 x 2 is the max

i.e. £1.03

Tricky question

Regards
SVE

Ok. We get it now. Thanks guys!

Or..

49*2 + 1*5 = 1.03
3*2 + 19*5=1.01

I suspect it is highest remainder for 100 by either 2 or 5 + 5 or 2

i.e 95+ 3*2 or 98+1*5

as they wanted highest it has to be 1.03
epp