Question

Two positive numbers have a product of 575. If the larger number is 2 more than the smaller, what are the numbers?

A) 23, 25
B) 15, 38
C) 19, 30
D) 25, 23

Answer 1

To solve the problem, we set up a quadratic equation and find the values of 'x' that satisfy the equation. The smaller number is 23 and the larger number is A)25.

Step-by-step explanation:

To solve this problem, let's represent the smaller number as 'x' and the larger number as 'x + 2'. We know that the product of these two numbers is 575, so we can set up the equation:

x(x + 2) = 575

Expanding and rearranging the equation, we get:

x^2 + 2x - 575 = 0

Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. Factoring gives us:

(x - 23)(x + 25) = 0

So the possible values for 'x' are 23 or -25. Since we are looking for positive numbers, the smaller number is 23 and the larger number is 23 + 2 = 25.