Question

The difference between two numbers is 17 and their sum is 69. Write the largest of these two numbers.

Answer 1

Answer-

X+y= 69

x-y= 17

let first number=x

another number=69-x

x(69-x)= 17

x-69+x=13

2x= 13+69

2x= 82

x= 41

so,

the numbers are

41

69-41=28

Answer 2

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

$\underline{ \mathfrak{ \: \: Suppose, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \text{The largest number be x} \\ \text{ And, } \\ \: \: \: \: \: \: \: \: \: \text{The smallest number be y} \\ \\ \\ \underline{\mathfrak{ \: \: Given, \: \: }} \\ \\ \: \: \: \text{ Difference between the two numbers = 17 } \\ \text{And, } \\ \: \: \: \text{Sum of the two numbers = 69 } \\ \\ \\ \underline{ \mathfrak{ \: \: To \: \: find :- \: \: }} \\ \\ \: \: \: \: \: \text{The \: \: largest \: \: number = ? }$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \mathtt{x - y = 17 \: \: \: - - - - - > (1)} \\ \\ \: \: \: \: \: \: \: \mathtt{x + y = 69 \: \: \: - - - - - > (2)}$

$\mathfrak{ \: \:Now, \: \: } \\ \\ \mathtt{(1) + (2) \Rightarrow \: 2x = 86} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ \Longrightarrow \: x = \frac{86}{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ \Longrightarrow \: x = 43 } \\ \\ \mathtt{ \therefore \: \: The \: \: largest \: \: number \: \: is = 43}</p><p>$

$\mathfrak{ \: \:Again, \: \: } \\ \\ \mathtt{</p><p>(2) - (1) \Rightarrow 2y= 52} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{\Longrightarrow \: y = \frac{52}{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{\Longrightarrow \: y = 26}</p><p> \\ \\ \mathtt{ \therefore \: \: The \: \: smallest \: \: number \: \: is = 26}$

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

$\: \: \: \: \text{The numbers are = 43 \: and \: 26} \\ \\ : \rightsquigarrow \: \text{Difference between the numbers = 43 \: - \: 26 =17 } \\ \\ : \rightsquigarrow \: \: \text{Sum of the numbers = 43 + 26 = 69}$