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Today the students learned a few tricks to help them when leaving tips or calculating discounts. One lucky winner was closest to guessing the price of a basket of stuff and won it all as a prize (world cup soccer ball, sudoku book, reading light, marker set, etc).

Class Materials - Strategy Review - Draw a Picture, Make A List. Guided

problem set⁠

to help everybody reinforce these topics on their own.

Extra MO Problems -

Here⁠

. Problems, problems with hints, and then solutions.

Upcoming Competitions - We can participate in a tournament Oct 26th in Irvine or Oct 27th in Temple City. Email me or gracefei2004@hotmail.com if interested.

Mailing List - Up to 61 subscribers, which feels like it might be the peak. Math loving friends can sign up

here⁠

or email me at rbarrows@alum.mit.edu

Math In The Real World (pdf for printing

here⁠

)

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Shopping
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Who likes shopping?

Who likes getting a good deal?

Who likes free stuff?

Who likes getting scammed and ripped off?

We'll figure out how to be sure we're getting a good deal and avoid the people who try to hide their ripoffs using fancy math.

Is it a good deal?

Imagine you're shopping and you see this sign on the door:

Going out of business, 40% off everything in the store.

Today only, takes an extra 30% off when you spend $100 or more!!!

Seems like a pretty good deal right? You're going to get $100 of stuff for only $30, right? Wrong in three ways, maybe more. Who can think of them?

1) You can't add the discounts!!! How much is "an extra 30% off" of something 40% off?

Like we often do, let's find an example that makes the math easy. $100 original price. What is it after 40% off? $60. Now can anyone take 30% of that in their head? [Mental Math Trick Here] Ignore the zeros, just multiply 3 * 6, which is $18, and then figure out if your decimal place is right. The answer might be 1.8 or 180, but by looking at it quickly you should see that 18 is correct. So what is the final price? $60 - $18 = $42. $42 isn't bad of course, but not nearly as good as $30.

2) They used tricky wording "when you spend $100" not "when you buy something that was originally $100". So how much do you have to buy, at the original price, to end up spending $100? Again, let's use easy math to simplify the problem. From above we know that for every $100 we end up spending $42. So $200 gives $84. It looks to me like we need to spend about $250, just a little less. The real math is to divide 100 by .42, which gives $238.10.

3) Don't forget about the tax. Tax is about 10% in California.

Who knows the easy way to calculate 10% tax? Just move the decimal point over by one.

While we're at it, who knows the easy way to calculate a reasonable tip to leave at a restaurant? Double the tax. Round up if service was good, round down if it was bad. This gives something like an 18-20% tip.

So your final cost for $238 of merchandise is $110. 53.8% percent off of the headline cost.

Supermarket Sweep

Whoever gets the closest answer in 60 seconds wins the basket!

$7.99 Sudoku Puzzle Book. TODAY ONLY take 20% off.

$14.95 Women's World Cup Soccer Ball

$8 Clip on reading light

$4 Gold pins and clips

$3.50 Rainbow assortment of pens. TODAY ONLY take 30% off.

What's the final bill, including 10% sales tax?

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⁠⁠ Shopping ⁠⁠

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Shopping
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