number puzzle

[bobobalde111]

how many of these new belts have we sold joe asked
i priced them at 14.95
not many sarah replied
ok drop the price by one pound tomorrow and one pound the next day if you think its advisable
some days later joe remembered the belts and asked about them
i cut the price twice as you said sarah told him
we've sold them all know and for a total of just 10p under 300.00
how many belts were sold

all help appreciated

[Aquagility]

32? (by trial, not enough information to construct a logical equation)

[bobobalde111]

how do you break that down
how many at each price

[Aquagility]

Sorry, 22 not 32.
i.e. 5 @ �14.95 = �74.75
5 @ �13.95 = �69.75
12 @ �12.95 = �155.40
Total �299.90
Q.E.D

[bobobalde111]

many thanks

[crofter]

Good Morning bob - There is a short cut by looking at the change! Suppose A belts were sold at �14.95 which can be take as �15.00 - 5p. Furthermore, suppose B belts were sold at �14.00 - 5p and C belts at �13.00 - 5p, then the amount of money they will have is given by the expression "15A + 13B + 13C - (A+B+C) 5 pence pieces".
But this is equal to �299.90 = �300 - two 5 pence pieces.
So we deduce that (A + B + C) = 2 or 22 or 42 or ...
(there being twenty 5 pence pieces to the pound)

Since the belts are selling for around �14 each and a quick check shows that 22 x �14 is close to �300, then the answer must be 22 belts sold!

A breakdown of sales day by day is not required so has been omitted.

[Aquagility]

Crofter, you are too clever by half!

[crofter]

Aquagility This will be my last year before retirement and I hold a PhD in Mathematics / Statistics. I have devoted my professional life to studying, applying and teaching Mathematics - spanning over 40 years of University study. In that time, you're bound to pick up a trick or two!

Having said that, I love helping out on AB and really look forward to bob's Tuesday morning poser! Over the years you become trained to see lines of analysis that others cannot see.

Nevertheless, I sometimes get things horrribly wrong. We're all human!

[bobobalde111]

many thanks for all the answers
your answers to the impossipuzzle have became a thing of legend in scotland amongst my friends

you truly deserve a long a happy retirement though not from ab

best wishes
bob (aka david)
do you know who the real bobo is
its a name i chose to spark interest

[Aquagility]

CROFTER - No wonder you get your sums right! But surely I. as a humble engineer, deserve some credit for getting the correct answer by empirical methods?
I read that Brunel had no knowledge of mathematics, which could account for the strength of his structures.

[crofter]

bobo balde is a 6' 3" French-African footballer who plays at the heart of the Celtic defence.

Although not Scottish, my father was a piper in the Cameronians throughout WW2, so I was raised steeped in Scottish culture. I still get a tingle when "I hear the pibroch sounding".

As for Aquagility, I give you every credit. My motto is "FIRST find a solution - THEN worry about whether or not it's elegant". There's quite a few ABers out there (like you) who are prepared to get stuck in to Mathematics. Excellent!

When I retire from academia, I should have even more time to spend on AB!

Cheers! crofter (aka David by the way)