Problem

**FreeRiderZ** · September 21st 2010, 09:11 AM

Hi everybody,

I'm French and I had my first mathematic class today.

I don't understand an exercise :

Can you help me ?

A brother and sister share out their collection of 5.000 stamps in the ration 5:3.
The brother then shares his stamps with his 2 friends in the ratio 3:1:1, keeping more for himself.
How many stamps do each of his friends receive ?

Thx a lot

**Traveller** · September 21st 2010, 09:16 AM

It means that if the brother has 5x stamps for some x, then the sister has 3x stamps.

After the brother shares his stamps with his friends, if the brother has 3y stamps for some y, then both of his friends have y stamps each. You have to find y.

**Soroban** · September 21st 2010, 12:43 PM

Hello, FreeRiderZ!

A brother and sister share out their collection of 5.000 stamps in the ration 5:3.

The brother then shares his stamps with two friends in the ratio 3:1:1,
keeping more for himself.

How many stamps do each of his friends receive ?

$\begin{array}{cccccc}<br /> \text{The brother got }5a\text{ stamps} \\<br /> \text{The sister got }3a\text{ stamps} \end{array}\;\text{ for some integer } a.$

There were 5,000 stamps: . $5a + 3a \:=\:5000$

. . $8a \:=\:5000 \quad\Rightarrow\quad a \:=\:625$

$\begin{array}{cccccc}\text{The brother got: }& 5a &=& 5(625) &=& 3125\text{ stamps.} \\<br /> \text{The sister got: }& 3a &=& 3(625) &=& 1875\text{ stamps.} \end{array}$

The brother divided his stamps into three groups: . $3b,\:b,\;b$

We have: . $3b + b + b \:=\:3125 \qiad\Rightarrow\quad 5b \:=\:3125 \quad\Rightarrow\quad b \:=\:625$

He gave his two friends 625 stamps each.
. . . (And kept 1875 stamps for himself.)

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