Percentages

[sherrardk]

What is the correct (ie current) method for explaining to my son how to answer the following question?

'a boy buys a football that has been reduced by 15% and now costs £4.25. How much did the ball cost originally?'

PS - he's 10.

Thanks

[factor-fiction]

Well, given that he's 10 it may be he's only expected to use trial and error (perhaps better called 'trial and improvement' ).
A good first guess is £5 for the initial price. Work out 10% of £5- that's 50p. Then work out 5%- that's half as much, or 25p. So total discount 75p.
That gets you straight to the answer

[DTCwordfan]

start with 10 pounds - if 10 pounds equals 100 percent, then some thing that has been reduced by 20% means that it is now 80 per cent of the original price, so 100% -20% = 80% and 80% is 0.8 of 1 or 80 of 100.

So what do we do is multiply 10 by 0.8 and we get £8.

Now apply that logic to the problem 4.25 = 100%. 100% - 15% = 85% so we multiply £4.25 by 0.85 and, voila, £3.61 is the answer

[jackthehat]

Original cost of ball (a) = 100%
Present cost (b, or £ 4.25) = 75%
Divide £ 4.25 by 75 - this will = 1%
Then multiply answer by 100 to get 100%, i.e. original cost.

[jackthehat]

D'oh!!

85 every time I said 75 I meant 85..................:o(

[factor-fiction]

Of course the standard approach taught would be to say the new price of £4.25is 85% of the old price.
So one percent of the old price is £4.25/85= £0.50
So 100% of the old price is 100 x £0.50 = £5

In one step the calculation is £4.25 x 100 /85 = £5

[Buenchico]

The method used for 10-year-olds nearly always relates to finding one per cent and working from there. So . . .

85% of the original price = £4.25
Divide by 85 to find that . . .
1% of the original price = £0.05
Multiply by 100 to find that . . .
100% of the original price = £5.00

Chris

[gingejbee]

DT: first rule of maths - read the question properly.

[DTCwordfan]

my apologies and not even drinking this month.....

[Prudie]

No DT, £4.25 is 85% of the orignal price
£4.25/85 = 1% = £0.05
so 100% = 100 x 0.05 = £5
for a 10 yr old factor's method is prob best

[Prudie]

I must learn to type faster

[factor-fiction]

I think DTcrosswordfan has misunderstood the question. The question asks what the original price was before the discount was applied. The answer is £5.

You have reduced the already discounted price by 15% which is not the question.

The teacher will expect the student to do this by trial and improvement. A good first gues is £5, and as I explained a 15% discount off £5 would be 75p- which brings the price down to the required figure of £4.25

[jackthehat]

<cough> testing.............testing..............are you receiving me ?..........

[factor-fiction]

hi jth- is your coughing directed at sherrardk or to some of us?

[sherrardk]

Thanks to all of you for your help - I will go through it with him tomorrow and see how he gets on.

[jackthehat]

I was just wondering if some of the other contributors had actually looked at my post..........or indeed if I alone could see it.............

[factor-fiction]

Hi jth- don't take it personally- it's a timing problem. Your solution post and subsequent correction would have appeared while several of us were part way through typing our answers.
I always look at your posts jth, but not always as soon as you've typed them

[R1Geezer]

the best way is the simple arithmetic way 4.25 has been multiplied by 0.85 so to get the start poit divide by 0.85, Far simpler than mucking about with iteration etc.
4.25/0.85 = 5

[factor-fiction]

Your arithmetic is of course correct RI Geezer and I would agree with that approach if student has a good grasp of what percentages are, recognises the link between 15% reduction and the figure of 0.85, and is able to divide by 0.85.
However in my experience it is unlikely that a ten year old will have a grasp of these concepts, and where he/she doesn't an iterative approach is a good starting point.

[sherrardk]

Thanks for your input - but the last two posts are above both of our heads (mine and the ten year olds). x

[factor-fiction]

I rest my case....
Goodnight all.