Final answer:
The original price of the television was $476, calculated by dividing the sale price of $238 by 0.50 since the television was on sale for 50% off.
Step-by-step explanation:
To find the original price of the television, we need to understand that the sale price represents 50% (or half) of the original price because the television was purchased after a 50% reduction.
If $238 is 50% of the original price, then to find the original price, we can set up the equation 0.50 × (original price) = $238. We solve for the original price by dividing $238 by 0.50.
The calculation would be: original price = $238 / 0.50 = $476.
Therefore, the original price of the television was $476.
Let
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P be the original price of the television. When the television is reduced by 50%, the sale price becomes 50% of the original price. Mathematically, this can be expressed as P \times (1 - 0.50) = $238, where
1
−
0.50
1−0.50 represents the remaining 50% after the reduction.
To find the original price
�
P, we can rearrange the equation as P = \frac{$238}{1 - 0.50}. Solving this gives P = $476.
Therefore, the original price of the television was $476. After applying a 50% reduction, the sale price of $238 represents half of the original cost, reflecting the discount. This calculation helps illustrate the relationship between the reduced price and the original price after a percentage reduction.