The sum of four consecutive odd numbers is 112.what are the numbers?
Let's represent the four consecutive odd numbers as x, x+2, x+4, and x+6.
According to the problem, the sum of these four numbers is 112.
x + (x+2) + (x+4) + (x+6) = 112
Simplifying the equation, we get:
4x + 12 = 112
Subtracting 12 from both sides:
4x = 100
Dividing both sides by 4:
x = 25
Therefore, the four consecutive odd numbers are 25, 27, 29, and 31.
To find the four consecutive odd numbers, we can follow these steps:
Step 1: Let's assume the first odd number as 'x.'
Step 2: The second consecutive odd number would be (x + 2) since consecutive numbers have a difference of 2.
Step 3: Similarly, the third consecutive odd number would be (x + 4), and the fourth consecutive odd number would be (x + 6).
Step 4: Now, let's form an equation to represent the sum of these four consecutive odd numbers: x + (x + 2) + (x + 4) + (x + 6) = 112.
Step 5: Simplify the equation: 4x + 12 = 112.
Step 6: Subtract 12 from both sides of the equation: 4x = 112 - 12 = 100.
Step 7: Divide both sides by 4: x = 100 / 4 = 25.
So, the first odd number is 25.
Now, we can find the rest of the numbers using the consecutive odd number pattern:
Second number = 25 + 2 = 27.
Third number = 25 + 4 = 29.
Fourth number = 25 + 6 = 31.
Therefore, the four consecutive odd numbers that add up to 112 are 25, 27, 29, and 31.
Let's solve this step-by-step.
Step 1: Represent the consecutive odd numbers
Let's assume that the first odd number is represented by "x". Since we are given four consecutive odd numbers, we can represent the other three consecutive odd numbers as "x + 2", "x + 4", and "x + 6".
Step 2: Set up the equation
The sum of the consecutive odd numbers is given as 112. So we can set up the equation as:
x + (x + 2) + (x + 4) + (x + 6) = 112
Step 3: Simplify the equation
Combine like terms:
4x + 12 = 112
Step 4: Isolate the variable
Subtract 12 from both sides of the equation:
4x = 100
Step 5: Solve for x
Divide both sides of the equation by 4:
x = 25
Step 6: Find the other three numbers
Now that we know the value of x, we can substitute it back into our equations to find the other three numbers:
First odd number: x = 25
Second odd number: x + 2 = 25 + 2 = 27
Third odd number: x + 4 = 25 + 4 = 29
Fourth odd number: x + 6 = 25 + 6 = 31
So the four consecutive odd numbers are 25, 27, 29, and 31.
x+x+1+x+3+x+5=112
x+x+x+x+1+3+5=112
4x+9=112
4x=112-9
4x=103
Divide but side by 4
4x/4=103/4
x=25.75
The numbers are 25.75,26.75,28.75,39.75
I apologize, but there seems to be a mistake in your calculations. Let's go through the steps again correctly.
Step 1: Represent the four consecutive odd numbers
Let the first odd number be x.
The second odd number would be x + 2.
The third odd number would be x + 4.
The fourth odd number would be x + 6.
Step 2: Set up the equation
x + (x + 2) + (x + 4) + (x + 6) = 112
Step 3: Simplify the equation
Combine like terms:
4x + 12 = 112
Step 4: Isolate the variable
Subtract 12 from both sides of the equation:
4x = 100
Step 5: Solve for x
Divide both sides by 4:
x = 25
Step 6: Find the other three numbers
Substitute the value of x into the consecutive odd numbers:
First odd number: x = 25
Second odd number: x + 2 = 25 + 2 = 27
Third odd number: x + 4 = 25 + 4 = 29
Fourth odd number: x + 6 = 25 + 6 = 31
Therefore, the four consecutive odd numbers that add up to 112 are 25, 27, 29, and 31.