The sum of 2 positive numbers is 151. the lesser number is 19 more than the square root of the greater number. what is the value of the greater number minus the lesser number?

To determine the value of the numbers described, we need to set up two equations since we have two unknowns. We do as follows:

let x = greater number

y = lesser number

sum of 2 positive numbers is 151: x + y = 151

the lesser number is 19 more than the square root of the greater number: y = 19 + √x

Solving,

x + 19 + √x = 151

x = 121

y = 30

Therefore, the value of the greater number minus the lesser number is 121-30 = 91.