A television's price was discounted $40\%$ and then slashed another $40\%$ during a liquidation sale. By what percent has the original price been reduced?
Let the original price of the television be $T$. Then the price is now $0.6(0.6T)=0.36T$. Thus overall the price has been reduced by $1-0.36=\boxed{64\%}$.
64\%
Level 3
Algebra
Problem: A television's price was discounted $40\%$ and then slashed another $40\%$ during a liquidation sale. By what percent has the original price been reduced?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the total percentage reduction from the original price after two successive discounts, we need to understand how percentage reductions compound. 

Let the original price of the television be represented as P. The first discount of 40% reduces the price to 60% of P. This can be calculated as follows:

First discount: 
Price after first discount = P - (0.40 * P) = 0.60 * P.

Next, we apply the second discount of 40% to the new price. This means we take 40% off the already discounted price of 0.60 * P. 

Second discount: 
Price after second discount = (0.60 * P) - (0.40 * (0.60 * P)) = (0.60 * P) * (1 - 0.40) = (0.60 * P) * 0.60 = 0.36 * P.

Now, we find the total reduction from the original price P to the final price of 0.36 * P. The reduction amount is:

Reduction amount = P - (0.36 * P) = 0.64 * P.

To express this reduction as a percentage of the original price, we calculate:

Percentage reduction = (Reduction amount / Original price) * 100 = (0.64 * P / P) * 100 = 64%.

Thus, the original price has been reduced by 64%.<|END_OF_LATENT|> The final answer is $64\%$.