The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find the numbers
Question 1 Report
The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find the numbers
Answer Details
Let the two consecutive whole numbers be x and x+1.
Then, according to the problem statement:
x + (x+1) = \(\frac{5}{6}\)(x(x+1))
2x+1 = \(\frac{5}{6}\)(x² + x)
Multiplying both sides by 6 to remove the fraction:
12x + 6 = 5x² + 5x
5x² - 7x - 6 = 0
Solving the quadratic equation above by factoring or using the quadratic formula, we get:
x = -1 or x = 1.2
Since we're looking for consecutive whole numbers, x must be 1.
Therefore, the two consecutive whole numbers are 1 and 2.
So the answer is (2, 3).
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