Finding the number of this percentage

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Croybhoy1981

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I've been doing revision for an upcoming exam and I'm stuck at this:


A prison guard left the door open,and now 64% of the prisoners from Ficshire Security Centre have escaped.There are 1560 prisoners left.How many prisoners were there originally? Work out your answer to the nearest whole prisoner.

Now I get that the 1560 remaining prisoners is equal to 36% So what I thought to do was find out 1% So I divided 1560/36 which gave me 43.3333 So I now multiplied this by 100 and got 4333

However in the answers at the rear of the book the explanation is as follows:

1602/36 = 44.5,which = 1%.So 44.5 x100 = 4450

Where on earth does the 1602 come from That is divided by 36?
 
Hello, and welcome to FMH! :)

I would let \(P\) be the number of prisoners originally. And then from the problem statement, we may write:

[MATH]P-0.64P=1560[/MATH]
Combine like terms:

[MATH]0.36P=1560[/MATH]
Divide through by 0.36:

[MATH]P=\frac{13000}{3}\approx4333[/MATH]
I think the solution in the back of your book is in error, not you.
 
Let x = number of prisoners.
x-.64x =1560
Croybhoy1981 said:
I've been doing revision for an upcoming exam and I'm stuck at this:


A prison guard left the door open,and now 64% of the prisoners from Ficshire Security Centre have escaped.There are 1560 prisoners left.How many prisoners were there originally? Work out your answer to the nearest whole prisoner.

Now I get that the 1560 remaining prisoners is equal to 36% So what I thought to do was find out 1% So I divided 1560/36 which gave me 43.3333 So I now multiplied this by 100 and got 4333

However in the answers at the rear of the book the explanation is as follows:

1602/36 = 44.5,which = 1%.So 44.5 x100 = 4450

Where on earth does the 1602 come from That is divided by 36?
Click to expand...
What you did is fine. Good job!

I have no idea where they got 1602 from
 
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