Let's break down the problem from the image step by step:

1. Maureen's Total Winnings: Let the total amount Maureen won be $x$.

2. Saved Half: Maureen saved half of her winnings, so she has spent the remaining half, $\frac{x}{2}$.

3. Spending on Furniture: Of the remaining half, one-third was spent on furniture. This amount is $\frac{1}{3} \times \frac{x}{2} = \frac{x}{6}$.

4. Spending on Television: The remaining amount was spent on a television worth 20,000 pesos. The remaining amount is the difference between the half that was left after saving, minus what was spent on furniture: $\text{Remaining for TV} = \frac{x}{2} - \frac{x}{6} = \frac{3x}{6} - \frac{x}{6} = \frac{2x}{6} = \frac{x}{3}.$ So, the amount she spent on the television is $\frac{x}{3} = 20,000$ pesos.

5. Solve for $x$: To find how much Maureen won in total, solve the equation: $\frac{x}{3} = 20,000$ Multiply both sides by 3: $x = 60,000 \text{ pesos}.$

Thus, Maureen won 60,000 pesos.

What part of the total amount was allocated to television?

The fraction of the total amount $x$ that was spent on the television is $\frac{x}{3}$. Therefore, one-third ($\frac{1}{3}$) of the total amount was allocated to the television.

The correct answer is: 1/3.

Would you like more details or explanations on any part of this solution? Here are some related questions for further practice:

1. If Maureen had won 100,000 pesos, how much would she have spent on furniture?
2. What fraction of her total winnings did Maureen save?
3. If the amount spent on the television was 25,000 pesos instead, how much did she win?
4. How much did Maureen spend on furniture if she spent one-third of her remaining money on it?
5. If the total amount saved and spent on furniture was 40,000 pesos, what was the total amount won?

Tip: When working with fractions and word problems, always try to define the total amount as a variable, like $x$, and express each part of the problem in terms of that variable to keep track of everything easily.