Question

One number is 4 more than 2 times another. Their product is 30. Find the numbers. The numbers are ? and ? or ?and ? .

Answer 1

Let the first number be x and y be the second.

Then we habe:

I) x - 4 = 2y

II) x*y = 30

We can rewrite equation I as:

x = 2y + 4

Applying this result on equation II, we have:

(2y + 4)*y = 30

2y² + 4y = 30

2y² + 4y - 30 = 0

y² + 2y - 15 = 0

$\begin{gathered} y_+=\frac{2+\sqrt[]{(2)^2-4\cdot1\cdot(-15)}}{2} \\ y_+=\frac{2+\sqrt[]{64}}{2} \\ y_+=\frac{10}{2} \\ y_+=5 \end{gathered}$

The second root is negative and don't satisfy equations I and II, then we can discard it.

Replacing y with 5 in equation I, we have:

x - 4 = 2*5

x = 2*5 + 4

x = 14