Question

the product of two consecutive positive numbers is 30. use x for the lower number. what is the lower number? equation?

Explanation:

Step1: Define the numbers

Let the lower number be \( x \), then the next consecutive positive number is \( x + 1 \).

Step2: Set up the equation

The product of the two numbers is 30, so we have the equation \( x(x + 1)=30 \).

Step3: Expand and rearrange the equation

Expanding the left side gives \( x^{2}+x = 30 \), and rearranging to standard quadratic form gives \( x^{2}+x - 30=0 \).

Step4: Factor the quadratic equation

We factor the quadratic as \( (x + 6)(x - 5)=0 \).

Step5: Solve for \( x \)

Setting each factor equal to zero gives \( x+6 = 0 \) or \( x - 5=0 \). Solving these, we get \( x=-6 \) or \( x = 5 \). Since we are looking for positive numbers, we discard \( x=-6 \).

Answer:

The lower number is \( 5 \).