Question

[50 pts] An even number, n, times the next consecutive number, n + 2, is equal to 168. Find the original number.

Answer 1

We are given:

An even number 'n', multiplied by the next consecutive even number is 168

Solving for n:

From the given statement, we can say that:

n(n+2) = 168                      [n multiplied by the next even number 'n+2']

n² + 2n = 168

n² + 2n - 168 = 0               [subtracting 168 from both sides]

We can see that we now have a quadratic equation, solving using splitting the middle term

n² + 14n - 12n - 168 = 0

n(n + 14) -12(n + 14) = 0      [factoring out common terms]

(n-12)(n+14) = 0

Here, we can divide both sides by either (n-12) OR (n+14)

Checking the result in both the cases:

(n + 14) = 0/(n-12)                     (n-12) = 0/(n+14)

n + 14 = 0                                 n - 12 = 0

n = -14                                      n = 12

Both these values are even and since we are not told if the number 'n' is positive or negative, both 12 and -14 are the possible values of n