## Welcome to H3 Maths

Blog Support for Growing Mathematicians

### The Magic of Number 9 and Coffee!

September10

Does this number 9 seem to be smiling at you? Well perhaps it is! At least it doesn’t look sad and there is a smile in the middle after all.

“In eight studies published from 1987 to 2004, prices ending in the magic number nine (\$1.99, 49 and so on) boosted sales by 24 per cent.

In an experiment done by University of Chicago and MIT, a catalogue was printed in three versions to test the psychological power of the “magic number nine”.

Each catalogue was sent to an identically sized sample. The control price was set at \$39. And in experimental versions, the identical item was tested at \$34 and \$44.

And guess what happened? There were more sales at \$39 than at either of the other prices — including the cheaper \$34.” (source: http://www.news.com.au). [Update, Oct 11: “Australian Apple users are set to pay more for their apps, with the tech giant set to raise prices by 15 per cent. The changes, first reported by Mac news source 9 to 5 Mac, mean an app costing \$1.29 would rise in price to \$1.49. Perhaps Apple know only too well the power of the 9?]

And, just when you thought the Mathematics behind consumer habits was that simple…

…”You walk into a Starbucks and see two deals for a cup of coffee. The first deal offers 33% extra coffee. The second takes 33% off the regular price. What’s the better deal?”

They’re about equal!” you’d say, if you’re like the students who participated in a new study published in the Journal of Marketing. And you’d be wrong. The deals appear to be equivalent, but in fact, a 33% discount is the same as a 50 percent increase in quantity. Math time: Let’s say the standard coffee is \$1 for 3 quarts (\$0.33 per quart). The first deal gets you 4 quarts for \$1 (\$0.25 per quart) and the second gets you 3 quarts for 66 cents (\$.22 per quart).

The upshot: Getting something extra “for free” feels better than getting the same for less. The applications of this simple fact are huge. Selling cereal? Don’t talk up the discount. Talk how much bigger the box is! Selling a car? Skip the MPG conversion. Talk about all the extra miles.” (from: http://www.theatlantic.com)

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#### Post Support

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]