Finding the Cheapest Furniture Price
The problem asks for the price of the cheapest furniture item given the average price of three items and the ratio of their prices.
Steps to Calculate the Cheapest Price
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Represent Prices using Ratio: Let the prices of the three furniture items be $3x$, $5x$, and $7x$, according to the given ratio $3 : 5 : 7$.
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Use the Average Price Formula: The average price is calculated as the sum of prices divided by the number of items. $ \text{Average Price} = \frac{\text{Sum of Prices}}{\text{Number of Items}} $ Given the average price is ₹5,310 and there are 3 items, we have:
$ ₹5,310 = \frac{3x + 5x + 7x}{3} $ -
Solve for the Variable ($x$): Combine the terms in the numerator: $ ₹5,310 = \frac{15x}{3} $ Simplify the fraction: $ ₹5,310 = 5x $ Now, isolate $x$ by dividing both sides by 5: $ x = \frac{₹5,310}{5} $ $ x = ₹1,062 $
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Calculate the Cheapest Item's Price: The cheapest item corresponds to the smallest ratio part, which is 3. Therefore, its price is $3x$. $ \text{Price of Cheapest Item} = 3 \times x $ $ \text{Price of Cheapest Item} = 3 \times ₹1,062 $ $ \text{Price of Cheapest Item} = ₹3,186 $
The price of the cheapest item is ₹3,186.
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