### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

### Matching Fractions, Decimals and Percentages

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

# Charlie's Money

##### Age 11 to 14 Short Challenge Level:

Splitting the money into parts
Charlie spent $\frac14$ of his money on a book. He could have done this by splitting his money into 4 equal parts and then spending 1 of them:

He then gave $\frac23$ of his remaining money to his brother. So since he had 3 equal parts left, he simply gave 2 of these to his brother:

Then he had £9 left. So each of the equal parts was worth £9.

So he must have started off with 4$\times$£9 = £36

Working backwards
After giving $\frac23$ of his money to his brother, Charlie has £9. So £9 is $\frac13$ of the amount of money Charlie had before he gave money to his brother.
So before he gave money to his brother, Charlie had £9$\times$3 = £27.

That means that after spending $\frac14$ of his money on a book, Charlie had £27. So £27 is $\frac34$ of the amount of money Charlie had before he bought the book.
So $\frac14$ of the amount of money Charlie had before he bought the book is £27$\div$3=£9.
So before he bought the book, Charlie had £9$\times$4 = £36.

Finding what fraction of his money Charlie has left
After he spent $\frac14$ of his money on a book, Charlie had $\frac34$ of his original money left.

Then he gave $\frac23$ of this $\frac34$ to his brother, leaving him with $\frac13$ of $\frac34$ of his original money.

$\frac13$ of $\frac34$ is equal to $\frac14$. So Charlie has $\frac14$ of his original money left.

So $\frac14$ of Charlie's original money is £9, so Charlie must have started off with 4$\times$£9 = £36.

Using algebra
Let the amount of money Charlie had at the beginning be $c$.

So he spent $\frac14c$ on a book, which left him with $\frac34c$.

Then he have $\frac23$ of $\frac34c$ to his brother, leaving him with $\frac13$ of $\frac34c$, which was $£9.$

So $\frac13\times\frac34c=£9\Rightarrow\frac14c=£9\Rightarrow c=£9\times4=£36.$
You can find more short problems, arranged by curriculum topic, in our short problems collection.