Farah wants to buy a television and a radio for her grandparents. On an Internet sales, the price of a television to a radio is 7 : 4. After a discount of $132 on each item, the price ratio of the television to radio becomes 25 : 13. What is the discounted price of the television?
Question
Farah wants to buy a television and a radio for her grandparents. On an Internet sales, the price of a television to a radio is 7 : 4. After a discount of $132 on each item, the price ratio of the television to radio becomes 25 : 13. What is the discounted price of the television?
Solution
To solve this problem, we need to follow these steps:
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Let's denote the original price of the television as 7x and the radio as 4x (since their price ratio is 7:4).
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After the discount, the price of the television becomes 7x - 132 and the price of the radio becomes 4x - 132.
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We know that the ratio of the prices after the discount is 25:13. So, we can write the equation: (7x - 132) / (4x - 132) = 25 / 13.
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Now, we need to solve this equation for x.
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Cross multiply to get rid of the fraction: 13*(7x - 132) = 25*(4x - 132).
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Simplify to get: 91x - 1716 = 100x - 3300.
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Rearrange to get: 9x = 1584.
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Solve for x: x = 1584 / 9 = 176.
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Now, we can find the discounted price of the television by substituting x = 176 into the equation 7x - 132, which gives us 7*176 - 132 = $1100.
So, the discounted price of the television is $1100.
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