The prouder of two whole numbers is 945 and are some is 62. What are the two numbers

The numbers are 27 and 35

Step-by-step explanation: The first step in finding the two unknown numbers is to represent them by A and B. The question indicates that the product of two numbers is 945, so we can write an expression that looks like this

A x B = 945 or simply put

AB = 945 —————(1)

Furthermore we are given that the sum of the two unknown numbers is 62, hence we can also write

A + B = 62 —————(2)

What we now have is a pair of simultaneous equations

We shall start with equation (2) and make A the subject of the formula. Therefore

A = 62 - B

Next we shall substitute for the value of A in equation (1)

AB = 945

(62 - B) B = 945

62B - B^2 = 945

We move every variable to the right hand side of the equation and that gives us

B^2 - 62B + 945 = 0

{Remember that when a negative value crosses to the other side of an equation it becomes a positive value, and vice versa}

What we now have is a quadratic equation. By factorizing 62B we arrive at

B^2 - 27B - 35B + 945 = 0

(B - 27) (B - 36) = 0

Therefore B - 27 = 0 or B - 35 = 0

Hence, B = 27 or B = 35

If B = 27, by substituting this into equation (2) we now have

A + 27 = 62

Subtract 27 from both sides of the equation

A = 35

Similarly if we take B to be equal to 35 and substitute this into equation (2), A will be equal to 27.

Therefore, the two numbers are 27 and 35.