Question

the sum of two number is 97 and one of them is greater than the other by 51. Find the numbers.​

Answer 1

Answer:

let the number be x

the other number is x+51

according to question x+(x+51) = 97

2x +51 = 97

2x = 97-51

2x = 46

x= 23

so one number is 23 and other is 23+51 = 74

Answer 2

Let the larger number be x and smaller number be y.

As per the first given condition,

x + y = 97 eq. no. (1)

As per the second condition,

Dividend = Divisor × Quotient + Remainder

x = y × 7 + 1

x = 7y + 1

x – 7y = 1 (2)

Subtracting (2) from (1),

x + y = 97

x – 7y = 1

(-) (+) (-)

8y = 98

y = 96/8

y = 12

Substituting y = 12 in equation (1)

x + y = 97

x + 12 = 97

x = 97 – 12

x = 85