Percentages - real world help!

[Neverender]

So, every month I pay in 80% of the Nursery bill and the government tops this up. Simple, you'd think? But, no. This month my maths went very squiffy.

Can anyone explain the attached? I don't get why it doesn't all add up to 20% or how I can work this out properly.

I'd like some logic to apply to this as it genuinely doesn't make sense to me (although I have no doubts it's correct!)

Thank you,
#shitatmaths

The last box shows the increase from 640 to 800 so 25% of 640 is 160. 20% of 800 is also 160

£160 is 20% of £800.

So is the nursery bill £800?

You pay 80% (£640) and the government pays the remaining 20% (£160)?

The bottom figure shows 160 (the difference between 640 and 800) as a percentage of 640

640 PLUS 25% (160) = 800

Switch the numbers in the bottom 2 boxes. You will then get -20% as your answer.

The first 2 are percentages of 800. The last one is a percentage of 640.

Draw yourself a little number line and it should help you see

Of you did "what is the percentage increase from 800 to 640 it should give you 20%.

Because 160 is 20% of 800 but 25% of 640.

The percentage increase doesn't add up to 20 but is 25% because when you do the increase you start at £640 and not at £800.

To get from 640 to 800 you add 160. 160 is NOT 20% of 640 but 20% of 800.

To increase 640 by 20% you would have to work out 20% of 640 and then add it to the 640. ( a quick 10 percent would be 64, two lots of 64 would be 128, 600+128= 728)

I hope this helps

The difference is 160. But 160 is a bigger percentage of 640 than it is of 800. So you can knock 20% off 800 to get down to 640, but you have to add 25% back on to get to 800, because the first time you're calculating a percentage of 800, but the second time, you're calculating a percentage of 640.

The % increase of 640.
1% of 640 is bigger than 1% of 800.

800 is 25% bigger than 640 (25% of 640 = 160. 160+640=800.)
640 is 20% smaller than 800 (20% of 800 = 160. 800-160=640)

As you can see 160 is 25% of 640, but 20% of 800.

Depending on the number your calculating the % from will determine the % values.

In this case those sums look right.

The last example is not relevant you are trying to work out 20% of 800 which is a different sum to 640 plus 20%. The top two calculations are what you need. Easy way to work out 20% in your head is to work out 10% and double it..

Because your percentage increase is the percentage of £640 that it has increased by, not the percentage of 800.

4 x 160 = 640 so 160 is 25% (or a quarter) of 640

5 x 160 = 800 so 160 is 20% (or one fifth) of 800

Does the govmt pay 20% of YOUR contribution? In which case you need to pay £666.67
If they pay 20% of the bill then you pay £640.
I can explain how to calculate if you tell me which version you use!

Arggggh! I'm going to have to read these tomorrow when I have some brain left, but does anyone understand why I don't get why the increase isn't 20% when this is the proportion they're paying.

I'm really not thick but this kind of maths screws with me completely.

Any diagrams gratefully received as the numbers on their own just don't make sense to me. Open to new ways of learning - I just want to understand it!

Sorry if I'm being really thick!

The first two calculations are fine - 20% of 800 is 160. You pay the remaining 640.

The third calculation is what is confusing you. % increase/decrease is calculated by comparing the difference (160) to the original amount (640 because you’ve put this in first). Basically, switch the 800 and the 640 round in the third calculation and it’ll say 20%.

Or ignore the third calculation altogether because that sort of calculation has nothing to do with what you’re working out. All you need to know is 20% = 160 and 80% = 640.

If the total bill is £800 and they pay 20%

Wow Tickety, so it's just that I had the numbers the wrong way round? I can't ask DM as she was a teacher and will give me hell!

Like I said in my message, please just check if the government pay 20% of your bill or 20% if your contribution. Happy to explain in a message if you let me know x

So the way I would imagine this is with fractions (I usually go for cakes).

20% is a fifth.

So we divide our cake into fifths. One fifth is the government 20% (£160). The other 4/5th (£640, 80% or 4x160) is our proportion.

The governments portion of cake is 1/5 of the total. But it’s also 1/4 of our 4/5s because 1/5 is 4x less than 4/5th. 1/4 is 25%, hence where the 25% comes from. This is the same as 20/80 = 1/4= 25%.

It depends if you are comparing the government contribution to the whole (20% of 100% = 20%) or of your portion (20% of 80% = 25%).

Oh and don't worry about this being confusing. LOTS of people find percentages challenging. For example if you take £100 and increase by 20%you get £120 but if you then decrease by 20% you get £96!

They pay 20% of the total bill

Teacherontherun why though?! 10% is £10, whatever way you look at it...isn't it?!

So, if every month I take the total bill, decide it by 5 and then deduct this from the total, that's how much we need to pay in?