The product of two positive consecutive numbers is 42. What is the smaller number?
The square root of 42 is about 6.5
To find the smaller number, let's break down the problem into steps.
Step 1: Understand the problem.
We are given that the product of two positive consecutive numbers is 42. We need to find the smaller number.
Step 2: Set up the equation.
Let's represent the smaller number as "x." Since the numbers are consecutive, the larger number can be represented as "x + 1" because it is always one more than the smaller number.
The product of the two numbers is 42, so we can set up the equation:
x * (x + 1) = 42
Step 3: Solve the equation.
To solve the equation, we multiply the terms:
x^2 + x = 42
Rearrange the equation:
x^2 + x - 42 = 0
Step 4: Factorize or use the quadratic formula.
We can factorize the quadratic equation or use the quadratic formula to find the values of x. In this case, let's factorize the equation:
(x + 7)(x - 6) = 0
From this, we get two possible solutions for x:
x + 7 = 0 or x - 6 = 0
To find the smaller number, we need to find the value of x. Since the numbers are positive, we discard the negative solution. Hence,
x = 6
Step 5: Find the smaller number.
The smaller number is represented by x, which we found to be 6. Therefore, the smaller number is 6.
In conclusion, the smaller number is 6.