Everyone who thinks maths is a piece of cake try this!!!?

Question

A mother wins a prize in a lottery and deciedes to share all the money between her children in the following way:
the first child recieves £100 and one tenth of what remains,
the second child recieves £200 and one tenth of what remains,
the third child recieves £300 and one tenth of what remains
the fourth child recieves £400 and one tenth of the remainder,
and so on.
after distributing her prize in this way she is not too surprised that all her children recieved the same amount. how much money did they each recieveand how many children does she have?

Everyone who thinks maths is a piece of cake try this!!!?
A mother wins a prize in a lottery and deciedes to share all the money between her children in the following way:
the first child recieves £100 and one tenth of what remains,
the second child recieves £200 and one tenth of what remains,
the third child recieves £300 and one tenth of what remains
the fourth child recieves £400 and one tenth of the remainder,
and so on.
after distributing her prize in this way she is not too surprised that all her children recieved the same amount. how much money did they each recieveand how many children does she have?

please give your answer and how you worked it out please.

thank you

Answer 1

they each get 1500, she has 4 children

you have to keep trying numbers until you get it to work

Answer 2

Expressing the problem in initial analytical terms, we have

C(x) = 100x + .1(T - A(x-1) - 100x), where
C(x) is the inheritance of child x,
C(0) = 0,
A(x-1) is the total inheritance already allocated to the first (x-1)children, and
T is the total estate. Now, add the constraint that each child recieves the same inheritance, and C(x) becomes simply C, and A(x-1) becomes
C(x-1). Now, the formula reads, with some simplification,

C= 100x +.1T +.1C -.1xC
Grouping C terms together and then multiplying through by 10, we have

C(x+9)=900x+T

Solving again for C, we have

C= (900x+T) / (x+9)

Now, C may not depend on x, because each child recieves the same inheritance, so we must eliminate all the x's above. We do this by factoring out 900 from the numerator:

C= 900(x+T/900) // (x+9)

To eliminate the x's, T/900 must equal 9, so the two paranthetical terms cancel. Therefore, T = 8100. Also, after cancelling, We are left with

C = 900, which conveniently proveides an answer to our 2nd question, and the number of children is then easy to find.

Answer 3

They each received 900 pounds, and there were nine children.

Let p = the amount of the lottery prize

The first child receives 100 + (p-100)/10
which is the same as 100 + 1/10 p -10 = 1/10 p +90

The second child receiveds 200 + (p-200-100-(p-100)/10)/10 which is the same as 200 + 1/10 p - 30 - 1/100 p + 1
= 171 + 1/10 p - 1/100 p

Set what the first child receives = what the second child receives and solve for p. p = 8100

Plug that into the equation and each child gets 900. 8100/900 is nine children.

Answer 4

the lottery prize is £8100 shared by nine children-well done mortgage!

there is another answer to this one-let's take another look at this

let n =the number of children and x = the prize money

each child gets the same =x/n

the children get the following
shares:
1st =100(n-(n-1))+((n-1)/n)(x/n)
2nd=100(n-(n-2))+((n-2)/n)(x/n)
nth =100(n-(n-n))+((n-n)/n)(x/n)
=100(n-0)+((0)/n)(x/n)=100n

therefore,
the last child(n) gets 100n =x/n

>>>> x=100n^2.........(1)

the first child gets x/n = 100+(x-100)/10.....(2)

therefore, substituting (1)into(2)

(100n^2)/n =100+(100n^2-100)/10
100n = 100+10n^2-10=10n^2+90

>>>10n^2 -100n+90 =0

n^2-10n+9=0...............(3)
(n-9)(n-1) =0

>>>>>> n=1 or n=9

substitute back into (1) x=100n^2 =100*1
or x=100*9^2 =8100

therefore, a single child gets all the £100 lottery
winnings or nine children share £8100-namely
£900 each

note:- when you get the expression x=100n^2,
you are always going to end up with a quadratic in
n of the form an^2+bn+c=0 when x is eliminated
and since b^2 is unlikely to equal 4ac,two different
answers have to occur

i hope that this helps

Answer 5

Say the amount she won is P.

1st child receives 100 + 1/10 * (P-100)

2nd child receives 200 + 1/10 (what remains)
= 200+ 1/10 (P - what first got - 200)
= 200 + 1/10( P - (100+1/10(P-100)) - 200)
= 200 + 1/10(P -

since all children get equal amounts, these two are equal.

Equate and solve for P

Answer 6

Assume first there are two children. Let the prize money = p, the amount the first child gets = C1 and the amount the second child gets = C2.

So we have:

C1 = 100 + 0.1(P-100) and
C2 = 200 +0.1(P-C1-200)
We now use the second equation and substitute the first
So C2 = 200 + 0.1(P - 100 - 0.1(P-100) - 200)
C2 = 200 + 0.1(0.9P - 290) = 171 + 0.09P

But C1 = C2 (each child receives the same)

so
100 + 0.1(P-100) = 171 + 0.09P
hence P = 8100 pounds

Using the very first equation nad substituting for P = 8100 we have:
C1 = 100 + 0.1(8100-100)
So C1 = 900
So each child receives 900 pounds

Therefore there are P/C1 = 8100/900 = 9 children

Hope that helps!

Answer 7

The woman won 8100 pounds and has nine children.

Start at the last child and work backwards. It is much easier. Each child gets a certain amount plus a tenth of the remainder. The last child will have no remainder, so he is going to be getting 90% of the pot left over after the previous child gets his initial amount, but prior to taking out his tenth.

Answer 8

I love how everyone has gone through and done all this math to determine the answer. However, if one takes a moment to read the question and write down all the given information there is another easier possibility.

She had one child and £100. (one tenth of nothing is nothing). So she clearly didn't win a very large lottery jackpot. Hahaha.

Answer 9

Sorry, the 8100/9 kids doesn't work.

1st Kid gets 100 + 1/10 of 8000 (800) = 900. OK

2nd Kid gets 200 + 1/10 of 8100-900 (720) = 920. How is that equal to first kid?

Answer 10

First child amount = Second child amount

100 + 0.1R = 200 + 0.1(0.9R - 200)

0.1R = 80 + 0.09R

0.01R = 80

R = 8000

So each person gets 100 + 0.1*8000 = 900.

Total winning of 100 + R = 8100.

How many kids? 8100/900 = 81/9 = 9

Answer 11

Cathy G...You forgot to remove the 200 ..

1st kid: 100+.1(8100-100)=900 and leaves 7200
2nd kid: 200+.1(7200-200)=900 and leaves 6300
3rd kid: 300+ .1(6300-300)=900 and leaves 5400
and so on....
Yep, it all works.