Question

The marker costs 1/3 as much as the pen. The pen costs 1/3 as much as the book. The book costs 1/3 as much as the game.

The price of the marker is what fraction of the price of the game?

Answer 1

The answer is
`(1)/(27)*g`

Explanation:

In order to determine the fraction of the price, we have to write all the relations between the prices of each stuff.

Let:

m=marker price

p=pen price

b=book price

g=game price

So,

`m=(1)/(3)*p\\p=(1)/(3)*b\\b=(1)/(3)*g`

Then,

`p=(1)/(3)*( (1)/(3)*g)\\m=(1)/(3)* ((1)/(3)*( (1)/(3)*g))\\m=(1)/(27) *g`

Finally, the price of the marker in fraction of the price of the game is
`(1)/(27)*g`

Answer 2

To answer the question above we must take note that based on the given, before reaching the price of the marker, the price of the game should be multiplied by 1/3 three times such that,
price of the marker = (price of the game) *(1/3)^3
price of the marker = (price of the game)(1/27)
Thus, the answer is 1/27.