Fiona and Greg play a number guessing game. Greg gives Fiona this hint about his two secret numbers, "The product of the two consecutive positive integers that i am thinking of is 11 more than their sum." What are Greg's numbers?
n and (n+1)
Star in Swedish :)
n(n+1) = 11 + n + (n+1)
n^2 + n = 2 n +12
n^2 - n - 12 = 0
(n-4)(n+3) = 0
try n = 4
then n+1 = 5
check:
4*5 = 20
4+5 = 9
sure enough, 20 = 9 + 11
I hate math
Okay thank you so much!
L bozo + Ratio
L + RATIO on GOD
To find Greg's numbers, let's break down the problem step by step:
Step 1: Assume that the two consecutive positive integers are represented by x and (x+1).
Step 2: According to the given information, the product of these two numbers is 11 more than their sum. Mathematically, this can be represented as:
x * (x+1) = (x + (x+1)) + 11
Step 3: Simplify the equation:
x^2 + x = 2x + 12
Step 4: Move all terms to one side of the equation:
x^2 + x - 2x - 12 = 0
Step 5: Combine like terms:
x^2 - x - 12 = 0
Step 6: Factor the quadratic equation:
(x - 4)(x + 3) = 0
Step 7: Set each factor equal to zero and solve for x:
x - 4 = 0 --> x = 4
x + 3 = 0 --> x = -3 (ignore because we want positive integers)
Step 8: Substitute the value of x back into the original equation to find the other number:
x + 1 = 4 + 1 = 5
Therefore, Greg's numbers are 4 and 5.