Question

Find two consecutive positive integers such that their product added to four times the smaller integer equals 36.

Answer 1

To find two consecutive positive integers such that their product added to four times the smaller integer equals 36, we can set up an equation and solve for x. Therefore, the two consecutive positive integers are 4 and 5.

Step-by-step explanation:

To find two consecutive positive integers such that their product added to four times the smaller integer equals 36, we can set up an equation.

Let's say the smaller integer is x. The next consecutive positive integer would be x+1.

According to the given information, their product added to four times the smaller integer equals 36:

x (x+1) + 4x = 36

Now, simplify the equation:

x² + x + 4x = 36

Combine like terms:

x² + 5x = 36

Subtract 36 from both sides:

x² + 5x - 36 = 0

This is a quadratic equation. We can either factor it or use the quadratic formula to find the solution. Factoring, we can rewrite it as:

(x + 9)(x - 4) = 0

Setting each factor equal to zero:

x + 9 = 0 or x - 4 = 0

Solving for x:

x = -9 or x = 4

Since we are looking for positive integers, we can discard the negative solution -9.

Therefore, the two consecutive positive integers are 4 and 5.