Fifteen minutes - Five puzzles

Jai Ganesh · 2006-03-02 22:40:02

1. A man was asked what price per 100 he paid for some apples.
His reply was as follows: "If they had been 4 cents more per 100 I should have got five less for $1.20."
Can you say what the price was per 100?

2. If a car had increased its average speed for a 180-mile trip by 5 mph, the trip would have been completed in 30 minutes less.
What was the car's original speed?

3. Complete the equation by filling in the five missing numbers with 4, 5, 6, 8, and 9.(Each number may be used only once.)

( _ + _ - _ ) X _ divided by _ = 1

4. Tony and Tommy have been experimenting with balloons.
They found that if they fill 5 balloons with helium, they can use the balloons to lift 50 pounds. Three of the same balloons filled with hydrogen lift 60 pounds. Ten filled with neon lift 20 pounds.
How many pounds could the men lift with 5 neon, one hydrogen, and two helium balloons?

5. A train, 0.25 miles long, going at a speed of 40mph enters a tunnel that is 2.25 miles long.
How long does it take for all of the train to pass through the tunnel from the moment the front enters it, to the moment the rear emerges?

Don't take more than fifteen minutes. Post your answers.

ashwil · 2006-03-02 23:52:23

1.

ashwil · 2006-03-03 00:39:25

2.

Jai Ganesh · 2006-03-03 02:43:31

good%20job.gif

mathsyperson · 2006-03-03 05:50:36

3.

Patrick · 2006-03-03 06:22:09

4.

Last edited by Patrick (2006-03-03 06:22:28)

mathsyperson · 2006-03-03 07:07:40

5.

ashwil · 2006-03-03 07:57:29

Patrick wrote:

4.

Patrick, if I bought the apples in question 1 at the correct price and, assuming the average apple weighs 100g, then sold you a pound for one pound, would you think it was a good deal for you or for me? How much profit or loss would I make?

Patrick · 2006-03-03 08:02:39

Ashwil - I'm not sure I'm getting you.. I wrote it for fun, because I don't know how many kg's there's on a pound...

Jai Ganesh · 2006-03-03 18:20:49

All correct answers! Well done, ashwil, patrick, mathsyperson!

patrick, the avoirdupois pound is 454 grams => 1 kilogram is 2.2026 pounds approximately.

ashwil · 2006-03-03 23:29:24

Don't worry Patrick. I was only joking with you. However, there is an important point within my joke. I am guessing that you are maybe one of the younger contributors here who has only learned metric units of measurement. The practical application of my (lame?) joke is actually very real. There are still large chunks of this world that insist on using imperial measurements such as pounds and miles. Equally, if you follow my example through, you will see that currency conversion also becomes a factor. The lesson is that the real world contains a myriad of situations where the ability to translate readily from one system to another AND to have some basic grasp of the relative scale of measurements can be a huge benefit. Let me give you a genuine example of how this can be useful.

For instance, I am a driver: I live in the UK. We now sell our petrol (gas) in litres, but we are still fixated on gallons and many older drivers still only think in gallons. I know that my car does about 35 miles per gallon (4.54 litres) and the price of the fuel is just over 90 pence per litre. In broad terms, this gives me a cost of 11p per mile. Now, I also travel frequently to the Philippines, where gas is priced in Pesos and sold in litres. The car only records distance travelled in kilometres. I know that the car does 10km per litre and that the cost is 30 Pesos per litre. The conversion rate of UK pound to Peso varies between about 90 and 100 Pesos to the pound.

Now, I can spend a long while working out exactly what my cost per distance travelled is, but, by having a good awareness of relative scale, I don't need to do that. Indeed, when I am driving, I am concentrating on driving, not on maths! Understanding the relative scales, tells me instantly that the price per litre in the Philippines is only 1/3 of the price in the UK. Hence, as long as the car in the Philippines has no major mechanical problem, I know that it is considerably cheaper to drive there than in the UK.

So, let's return to the apples:

In ganesh's problem, I get 100 apples (at 100g each) for 96 cents. 1 lousy cent each! I am proposing to sell you one pound weight for one pound Sterling. Say £1 = $1.70, then I am offering you approximately 4 1/2 apples for $1.70 when they only cost me 4 cents. In other words, I am ripping you off big time.

So, if you are still studying, then study well and learn the system you are being taught, but don't forget WHY mathematics is important. Understanding relative scale and the art of approxmation are vital skills in everyday life.

Patrick · 2006-03-03 23:45:35

Well, I still think we're talking about different things My comment wasn't towards #1, but #4 (the one I answered)... I do know how to compare different measurements to each other... You took my statement seriously, when you actually shouldn't But it's nice to see you're willing to explain something if others have problems understanding it.. Even though I actually didn't..

Math Is Fun Forum

#1 2006-03-02 22:40:02

Fifteen minutes - Five puzzles

#2 2006-03-02 23:52:23

Re: Fifteen minutes - Five puzzles

#3 2006-03-03 00:39:25

Re: Fifteen minutes - Five puzzles

#4 2006-03-03 02:43:31

Re: Fifteen minutes - Five puzzles

#5 2006-03-03 05:50:36

Re: Fifteen minutes - Five puzzles

#6 2006-03-03 06:22:09

Re: Fifteen minutes - Five puzzles

#7 2006-03-03 07:07:40

Re: Fifteen minutes - Five puzzles

#8 2006-03-03 07:57:29

Re: Fifteen minutes - Five puzzles

#9 2006-03-03 08:02:39

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#10 2006-03-03 18:20:49

Re: Fifteen minutes - Five puzzles

#11 2006-03-03 23:29:24

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#12 2006-03-03 23:45:35

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