On Friday I posted this puzzle….

A man spends a fifth of what is in his wallet, and then one fifth of what remained. He has spent a total of £72. What was the amount originally in his wallet?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.

The man originally had £200 in his wallet! Did you solve it?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle**(UK here and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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yep 🙂

100% – 20% = 80%

100% (80%) – 20% = 64%

so 36% = 72,- and 100% = 200,-

too easy…………

Nice bit of maths

No comment.

Looks a nice piece of thinking — except the answer surely is £112.50

Sorry thinking about the wrong part of the question. Go back to school

Yes.

100% – 20% = 80%

80% of 80% = 64%

Then: 100% – 64% = 36% (the amount remaining in the wallet £72)

So £72 is 36% of what the original amount was.

Therefore there was £200 in the wallet originally.

oops, not the amount remaining in the wallet, rather the amount spent out of the wallet. There’s actually £128 still in the wallet.

Whatever happened to good ol’ algebra?

O.2x + (0.8x * 0.2)=72

0.2x + 0.16x = 72

0.36x = 72

X = 200

Some of us don’t need it to do such simple maths is all that happened.

Yes, got it. Liked the puzzle, because took some time to get to the answer, and there was only one answer. It was also solvable without language problems.

Cool to see people thinking in %, It seems much simpler/ obvious now, but I did it with algebra:

(X/5)+((X4/5)/5)=72

(X+X4/5)/5=72

Multiply both sides with 5

X5/5+X4/5=X9/5=360

X=360/(9/5)=360/9*5=40*5=200

X=200

yup, 72 was 9/25 of original, ta for spelling it out.

I did it with algebra too, but not quite the same way.

1/5 + (1/5 * 4/5) = £72

1/5 + 4/25 = 5/25 + 4/25 = 9/25 = £72

So 1/25 = £72/9 = £8

So 25/25 = £8 * 25 = £200

You can do it in your head without all these math equations.

Start with 25/25ths – remove a fifth = 20/25 remaining, remove a fifth, that is four more. So we have taken 9/25ths which is = 72. If 9/25 x X = 72 then x = 72/9 x 25 = 8 x 25

That’s true. But how did you know to start with 25/25?

1/5 * 1/5 = 1/25

Yet I see equations in your solution. Just because you don’t write them on a piece of paper, parchment or carve them in stone does not mean you are not using equations

I used algebra too, and as soon as I saw the answer I realized that I should have intuitively known it by noticing that 72 is the sum of 40 and 32. My 9-year-old son saw it that way, and got it instantly.

Excellent!

I also came to the conclusion that he originally had 112,50.

For 72,- are 4/5 of what he had in his wallet in step one:

72:4 = 16; 16*5 =90

So before spending 1/5 he had 90,-

Again 90,- are 4/5 of what he originally had.

90:4= 22,5; 22,5*5 =112,50.

Let’s assume he had 112,50 and spends 1/5

112:50/5 = 22,5

112:50-22,5=90

Now he still has 90,- and again spends 1/5

90/5 = 18

90-18 = 72

QED

Now lets assume he had 200,- and spends 1/5

200:5 = 40

200-40 = 160

So now he has 160 ,-

If he again Spends 1/5 he still has

160:5 = 32

160-32 = 128,- left in his wallet.

128≠72

Therefore the answer 200,- is incorrect.

£72 is the amount he spent, not the amount left in the wallet.

Brilliant math! Reading comprehension…not so much :=(

Point taken… 😉

My calculations show that it is also possible the answer to be 300 !!

See: X/5+X/(5×5)=72 >> 6X/25=72 >> X=(72×25)/6 >> X=300 !!

And to prove it: 300/5=60 .. and 60/5=12 .. so 12+60=72 !!

Your second fraction is incorrect. It should be 4X/(5 • 5) since only 4/5 of the original amount remains in the wallet before spending the second 1/5.

X/5 + 4X/(5 • 5) = 72

5X/25 + 4X/25 = 72

9X/25 = 72

9X = 1800

X = 200

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Can anyone tell me if this is appropriate to be given to a Year 5 kid?