Answer:
One number is 29, and the other one 45
Step-by-step explanation:
Solve this problem by creating two equations that represents the statements, and solve for the unknowns using substitution:
Let's say that one of the numbers is X , and the other one Y, and assume that Y is larger than X, so when we do their difference we get the 16 units they mention in the problem:
Y - X = 16
The info on the product of the two numbers will give us our second equation:
X * Y = 1305
Now use the first equation to substitute Y with 16 + X, in the second equation:
X (16 + X) = 1305
16 X + X^2 = 1305
X^2 + 16 X - 1305 = 0
Now use the quadratic formula to solve for X, and we get two possible answers: X = -45 or X = 29
So, since we are looking for whole numbers, we discard the negative answer, and keep X = 29
Then, the value of the other number "Y" is = 29 + 16 = 45
