The product of two numbers is 1856. The sum is ninety. What is the difference of these two numbers? A. 30 B. 28 C. 26 D. 24

Let's solve this step by step:

Step 1: We know that the product of two numbers is 1856 and their sum is 90. Let's denote these two numbers as x and y. So, we have two equations:

x*y = 1856 x + y = 90

Step 2: We can express y in terms of x from the second equation:

y = 90 - x

Step 3: Substitute y in the first equation:

x * (90 - x) = 1856 90x - x^2 = 1856 x^2 - 90x + 1856 = 0

Step 4: This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a):

x = [90 ± sqrt((90)^2 - 4*1856)] / 2 x = [90 ± sqrt(8100 - 7424)] / 2 x = [90 ± sqrt(676)] / 2 x = [90 ± 26] / 2

Step 5: So, the solutions are x = 58 and x = 32. These are the two numbers.

Step 6: The difference between these two numbers is 58 - 32 = 26.

So, the answer is C. 26.