Answer: 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.
