Question

The sum of two numbers is 69 their difference is 39 what are the numbers

Answer 1

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Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Suppose, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \text{The largest number be x} \\ \text{ And, } \\ \: \: \: \: \: \: \: \: \: \text{The smallest number be y} \\ \\ \\ \underline{\mathfrak{ \: \: Given, \: \: }} \\ \\ \: \: \: \text{ Difference between the two numbers = 39 } \\ \text{And, } \\ \: \: \: \text{Sum of the two numbers = 69 } \\ \\ \\ \underline{ \mathfrak{ \: \: To \: \: find :- \: \: }} \\ \\ \: \: \: \: \: \text{The \: \: numbers = ? }$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \mathtt{x - y = 39 \: \: \: - - - - - > (1)} \\ \\ \: \: \: \: \: \: \: \mathtt{x + y = 69 \: \: \: - - - - - > (2)}$

$\mathfrak{ \: \:Now, \: \: } \\ \\ \mathtt{(1) + (2) \Rightarrow \: 2x = 108} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ \Longrightarrow \: x = \frac{108}{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ \Longrightarrow \: x = 54 } \\ \\ \mathtt{ \therefore \: \: The \: \: largest \: \: number \: \: is = 54}</p><p>$

$\mathfrak{ \: \:Again, \: \: } \\ \\ \mathtt{</p><p>(2) - (1) \Rightarrow 2y= 30} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{\Longrightarrow \: y = \frac{30}{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{\Longrightarrow \: y = 15}</p><p> \\ \\ \mathtt{ \therefore \: \: The \: \: smallest \: \: number \: \: is = 15}$

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: VERIFICATION \: \: } \mid}}}}}$

$\: \: \: \: \text{The numbers are = 54 \: and \: 15} \\ \\ : \rightsquigarrow \: \text{Difference between the numbers = 54 \: - \: 15 = 39 } \\ \\ : \rightsquigarrow \: \: \text{Sum of the numbers = 54 + 15 = 69}$