Question

Two consecutive odd whole numbers have a product of 483. What is the smaller of the two numbers?

Answer 1

Answer:

21 and 23

Step-by-step explanation:

let the odd number be x

the consecutive odd number will be x + 2

product of the two consecutive odd numbers is 483

x × (x + 2) = 483

$x \times (x + 2) = 483 \\ {x}^{2} + 2x = 483 \\ {x}^{2} + 2x - 483 = 0 \\ {x}^{2} + 23x - 21x - 483 = 0 \\ x(x + 23) - 21(x + 23) = 0 \\ (x + 23)(x - 21) = 0 \\ x + 23 = 0 \: \: \: \: \: x - 21 = 0 \\ x = - 23 \: \: \: \: \: x = 21$

we take the positive value of x

the consecutive odd numbers are

x = 21

x + 2 = 21 + 2 = 23

therefore the numbers are 21 and 23

Hope you get your answer