Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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Problem



 

We have a game which has a number of discs in seven different colours. These are kept in a flat square box with a square hole for each disc. There are $10$ holes in each row and $10$ in each column. So, there would be $100$ discs altogether, except that there is a square booklet which is kept in a corner of the box in place of some of the holes.

We haven't drawn a grid to show all the holes because that would give the answer away!



 

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Fractions in a Box



There is a different number of discs of each of the seven colours.

Half ($\frac{1}{2}$ ) of the discs are red, $\frac{1}{4}$ are black and $\frac{1}{12}$ are blue.

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Fractions in a Box



 

One complete row (of $10$ holes) of the box is filled with all the blue and green discs.

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Fractions in a Box



 

One of the shortened rows (that is where the booklet is) is exactly filled with all the orange discs.

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Fractions in a Box



 

Two of the shortened rows are filled with some of the red discs and the rest of the red discs exactly fill a number of complete rows (of $10$) in the box.

There is just one white disc and all the rest are yellow.

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Fractions in a Box



 

How many discs are there altogether?

What fraction of them are orange?

What fraction are green? Yellow? White?