Find four consecutive odd numbers that add up to 240. Explain your steps in order to receive partial credit in the event that your answer is not correct!
The Correct Answer and Explanation is:
To find four consecutive odd numbers that add up to 240, we can follow these steps:
Step 1: Define the Variables
Let the first odd number be represented by xxx. Since the numbers are consecutive odd numbers, the next three odd numbers can be expressed as:
- The second number: x+2x + 2x+2
- The third number: x+4x + 4x+4
- The fourth number: x+6x + 6x+6
Step 2: Set up the Equation
Now, we know that the sum of these four numbers is 240, so we can write the equation:x+(x+2)+(x+4)+(x+6)=240x + (x + 2) + (x + 4) + (x + 6) = 240x+(x+2)+(x+4)+(x+6)=240
Step 3: Simplify the Equation
Combine like terms on the left-hand side:4x+12=2404x + 12 = 2404x+12=240
Step 4: Solve for xxx
Now, subtract 12 from both sides to isolate the term with xxx:4x=240−124x = 240 – 124x=240−124x=2284x = 2284x=228
Next, divide both sides by 4:x=2284=57x = \frac{228}{4} = 57x=4228=57
Step 5: Find the Four Consecutive Odd Numbers
Now that we know x=57x = 57x=57, we can find the four consecutive odd numbers:
- The first number is x=57x = 57x=57
- The second number is x+2=57+2=59x + 2 = 57 + 2 = 59x+2=57+2=59
- The third number is x+4=57+4=61x + 4 = 57 + 4 = 61x+4=57+4=61
- The fourth number is x+6=57+6=63x + 6 = 57 + 6 = 63x+6=57+6=63
Step 6: Verify the Sum
Now, add the four numbers together to verify the sum:57+59+61+63=24057 + 59 + 61 + 63 = 24057+59+61+63=240
Thus, the four consecutive odd numbers that add up to 240 are 57, 59, 61, and 63.
Explanation:
- I started by defining the first number as xxx, then expressed the next three consecutive odd numbers in terms of xxx.
- I set up an equation based on the fact that the sum of the numbers is 240.
- I solved the equation step by step to find the value of xxx, and then substituted that value back to find the actual numbers.
- Finally, I checked the solution by summing the numbers to ensure the answer is correct.
