Interesting Maths Questions from the Missus

[sassthathoopie]

So here's a thought that my wife was just pondering while pouring the coffee. It's been a long time since my maths 'A' level and I wasn't able to give an answer that satisfied either of us so I'm hoping someone here can give us a good answer!

Emma paid £2.00 for a box of satsumas.

If the box contained 10 satsumas the price per satsuma would be £2.00/10 = £0.2 or 20p

If the box contained 20 satsumas the price per satsuma would be £2.00/20 = £0.1 or 10p

If the box contained 15 satsumas the price per satsuma would be £2.00/15 = £0.1333 or 13p

Her logic suggested that the unit price for 15 satsumas should be 15p. (Halfway between 10p and 20p) Clearly this isn't the case.

My thought was that there would be a gradient that wasn't 1:1 but was shallower.

But when I plotted a 5 pointed graph of unit price between 10p and 20p it was curved not linear!

What's going on?!

[sjg]

https://en.wikipedia.org/wiki/Exponential_decay

The more satsumas, the closer you'll go to zero per unit. If it was linear it would go negative instead.

[sassthathoopie]

Thank you!

I didn't spot the complete nature of the graph because I didn't plot enough satsumas!

[havoc]

sassthathoopie said:

it was curved not linear!

What's going on?!

You're dealing with factors / multiplication.

100 x 1 = 100
10 x 10 = 100

But
100 + 1 >>>> 10 + 10

Which is to say, as the graph above demonstrates, that while addition is linear, multiplication is exponential.

[Benrad]

And this is why you shouldn't extrapolate from two points to draw a straight line (or indeed interpolate!)

You'd have very quickly been paying people to take away for satsumas

Jordan Ellenburg's book, How not to be wrong, has some great real world examples of this

[J4CKO]

Hmm, Emma's planned role play of the horny Grocer and sexy customer took a very unexpected and unwelcome turn when the graph paper came out...

[TwigtheWonderkid]

sassthathoopie said:

So here's a thought that my wife was just pondering while pouring the coffee. It's been a long time since my maths 'A' level and I wasn't able to give an answer that satisfied either of us so I'm hoping someone here can give us a good answer!

Emma paid £2.00 for a box of satsumas.

If the box contained 10 satsumas the price per satsuma would be £2.00/10 = £0.2 or 20p

If the box contained 20 satsumas the price per satsuma would be £2.00/20 = £0.1 or 10p

If you carry on like that, it continues in the same fashion.

40 = 5p
80 = 2.5p
160 = 1.25p

& so on.

[SS2.]

J4CKO said:

Hmm, Emma's planned role play of the horny Grocer and sexy customer took a very unexpected and unwelcome turn when the graph paper came out...

[Monkeylegend]

Somebody is taking the pith.

[WyrleyD]

J4CKO said:

Hmm, Emma's planned role play of the horny Grocer and sexy customer took a very unexpected and unwelcome turn when the graph paper came out...

....and there was an audible gasp when he showed her is pencil and placed it on the table....

[andy_s]

J4CKO said:

Hmm, Emma's planned role play of the horny Grocer and sexy customer took a very unexpected and unwelcome turn when the graph paper came out...

[mr_spock]

Monkeylegend said:

Somebody is taking the pith.

Quite an apeeling problem

[Shakermaker]

Did your missus arrange the price structure for the Christmas cards I have arranged to buy from my daughter's childminder?

1 pack of 12 cards: £6

2 packs of 12 cards: £10

3 packs of 12 cards: £18

4 packs of 12 cards: £22


But you can specify the quantity of the number of sets that you want at each price point.

[PugwasHDJ80]

Shakermaker said:

Did your missus arrange the price structure for the Christmas cards I have arranged to buy from my daughter's childminder?

1 pack of 12 cards: £6

2 packs of 12 cards: £10

3 packs of 12 cards: £18

4 packs of 12 cards: £22


But you can specify the quantity of the number of sets that you want at each price point.

That's amazing - well done that girl

Increasing GP with volume- it is of course the answer.

Perhaps this is actually a SaaS model of card production?

[JuniorD]

andy_s said:

J4CKO said:

Hmm, Emma's planned role play of the horny Grocer and sexy customer took a very unexpected and unwelcome turn when the graph paper came out...

[Ari]

J4CKO said:

Hmm, Emma's planned role play of the horny Grocer and sexy customer took a very unexpected and unwelcome turn when the graph paper came out...

[PositronicRay]

Or the bloke on the market the other day.

£3 each 3 for a tenner.

[Ayahuasca]

Shakermaker said:

Did your missus arrange the price structure for the Christmas cards I have arranged to buy from my daughter's childminder?

1 pack of 12 cards: £6

2 packs of 12 cards: £10

3 packs of 12 cards: £18

4 packs of 12 cards: £22


But you can specify the quantity of the number of sets that you want at each price point.

Jason Rees-Mogg would never take the 3 pack offer.

[anonymous-user]

I buy satsumas in a net type thing or loose
Never in a box

[Monkeylegend]

techiedave said:

I buy satsumas in a net type thing or loose
Never in a box

But you have never been on The Apprentice.