Question

The difference of the age of the two brothers is 4 years and the product of their ages is 221. Determine the age of the two brothers

Answer 1

Given

• The difference of the age of the two brothers is 4 years and the product of their ages is 221.

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To find

• The age of two brothers.

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Solution

• Let the first brother's age be x and second brother's age be y.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{According\: to\: the\: Question}}}$

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$\tt\longrightarrow{x - y = 4}$⠀⠀... [1]

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$\tt\longrightarrow{xy = 221}$

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$\tt\longrightarrow{y = \dfrac{221}{x}}$

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Putting the value of y in [1]

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$\tt\longrightarrow{x - \dfrac{221}{x} = 4}$

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$\tt\longrightarrow{x = 4 + \dfrac{221}{4}}$

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$\tt\longrightarrow{x = \dfrac{4x + 221}{x}}$

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$\tt\longrightarrow{x^2 = 4x + 221}$

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$\tt\longrightarrow{x^2 - 4x - 221 = 0}$

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$\tt\longrightarrow{x^2 - 17x + 13x - 221 = 0}$

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$\tt\longrightarrow{x(x - 17) + 13(x - 17) = 0}$

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$\tt\longrightarrow{(x - 17) (x + 13) = 0}$

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• We get

→ x = 17 or -13

[Since, age can't be negative. Therefore we will take x = 17]

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Putting the value of x in [1]

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$\tt\longrightarrow{17 - y = 4}$

$\tt\longrightarrow{y = 17 - 4}$

$\tt\longrightarrow{y = 13}$

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Hence,

• Age of first brother is 17 years.
• Age of second brother is 13 years.