Number problem solving 2

Question:

The product of two consecutive positive number is 240. Find these two numbers.

Solution:

240 ÷ 2 = 120

120 ÷ 2 = 60

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 3 = 5

so 240 = (2)(2)(2)(2)(3)(5) = 2⁴ × 3 × 5

since 2⁴ = 16 and 3 × 5 = 15

so, 240 = 15 × 16

so, the two consecutive positive numbers are 15 and 16.

Use the quadratic equation to solve this problem. Because these two numbers are consecutive numbers, so if the first number is x, then he second number is (x + 1). Because the product of the two consecutive number is 240, so x(x + 1) = 240. Then x² + x = 240. Since the equation is two degrees of the variable x, so move the number 240 to the left side of the equation. We get the quadratic equation: x² + x - 240 = 0. The left side of the equation can be factored as (x - 15)(x + 16) = 0. Then (x - 15) = 0 or (x - 16) = 0. Thus, we get two solutions x₁ = 15 and x₂ = 16. So, these two consecutive numbers are 15 and 16.