One-quater of the sum of two consecutive odd numbers is 14.find the old numbers
Let's represent the two consecutive odd numbers as (2n-1) and (2n+1), where n is an integer.
The sum of these two numbers is:
(2n-1) + (2n+1) = 4n
Now, let's find one-quarter of this sum:
(1/4)(4n) = n
According to the problem, n is equal to 14.
So, the two consecutive odd numbers are:
(2*14-1) = 27 and (2*14+1) = 29.
Therefore, the odd numbers are 27 and 29.
Let's assume that the first odd number is "x", and the next consecutive odd number is "x + 2".
According to the question, one-quarter of the sum of these two numbers is equal to 14.
So we can write the equation:
(1/4) * (x + (x + 2)) = 14
Let's simplify this equation:
(1/4) * (2x + 2) = 14
Now, let's remove the parentheses and continue simplifying:
(1/4) * 2x + (1/4) * 2 = 14
(1/2)x + 1/2 = 14
Next, we can subtract 1/2 from both sides of the equation to isolate the term with x:
(1/2)x = 14 - 1/2
(1/2)x = 27/2
To get rid of the fraction, we can multiply both sides of the equation by 2:
2 * (1/2)x = 2 * (27/2)
x = 27
So the first odd number is 27.
To find the next consecutive odd number, add 2:
27 + 2 = 29
Therefore, the two consecutive odd numbers are 27 and 29.
To solve this problem, we need to follow a step-by-step approach. Let's break it down:
Step 1: Understand the problem.
We are given that the sum of two consecutive odd numbers is equal to one-quarter of this sum. We need to find the two odd numbers.
Step 2: Represent the unknowns.
Let's assume the first odd number is represented by "x" and the second odd number is represented by "x + 2" since they are consecutive odd numbers.
Step 3: Translate the problem into equations.
We know that one-quarter of the sum of these two numbers is equal to 14. So, we can set up the equation as follows:
(1/4) * (x + (x + 2)) = 14
Step 4: Solve the equation.
Let's simplify the equation:
(1/4) * (2x + 2) = 14
(1/4) * (2(x + 1)) = 14
(x + 1) = 14 * 4 / 2
(x + 1) = 7 * 4
(x + 1) = 28
x = 28 - 1
x = 27
Step 5: Find the second odd number.
To find the second odd number, we can substitute the value of x back into our assumption.
Second odd number (x + 2) = 27 + 2 = 29
Step 6: Verify the solution.
Now, we can check if our solution is correct by calculating one-quarter of the sum of these two numbers:
(1/4) * (27 + 29) = (1/4) * 56 = 14
Step 7: Answer the question.
The two consecutive odd numbers are 27 and 29.