The product of two consecutive integer is 5 three times the larger integer, what are the integers?
how's that again?
The product of two consecutive integer is 5 three times the larger integer
To solve this problem, let's start by setting up equations based on the given information.
Let's assume that the smaller integer is represented by "x". The next consecutive integer would be "x + 1".
According to the problem, the product of these two consecutive integers is 5 three times the larger integer, which can be expressed as:
x * (x + 1) = 5 * 3 * (x + 1)
Now, we can solve this equation step by step:
x(x + 1) = 15(x + 1) [distributing 5 and 3]
x^2 + x = 15x + 15 [multiplying]
x^2 + x - 15x - 15 = 0 [combining like terms]
x^2 - 14x - 15 = 0 [simplifying]
Now, we can solve this quadratic equation by factoring or using the quadratic formula:
Factoring:
(x - 15)(x + 1) = 0
So, either (x - 15) = 0 or (x + 1) = 0
If (x - 15) = 0, then x = 15
If (x + 1) = 0, then x = -1
Therefore, the two possible integers are 15 and -1.