The sum of five consecutive odd numbers is equal to 245.what is the difference between twice the largest odd number and the smallest odd number?
Question
The sum of five consecutive odd numbers is equal to 245.what is the difference between twice the largest odd number and the smallest odd number?
Solution 1
Sure, let's solve this step by step:
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We know that the sum of five consecutive odd numbers is 245. So, we can write this as: n + (n+2) + (n+4) + (n+6) + (n+8) = 245. Here, n is the smallest odd number.
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If we simplify this, we get: 5n + 20 = 245.
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Solving for n, we subtract 20 from both sides: 5n = 225.
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Then, we divide both sides by 5: n = 45. So, the smallest odd number is 45.
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The largest odd number would be n + 8 = 45 + 8 = 53.
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The difference between twice the largest odd number and the smallest odd number is: 2*53 - 45 = 106 - 45 = 61.
So, the difference between twice the largest odd number and the smallest odd number is 61.
Solution 2
Sure, let's solve this step by step:
-
We know that the sum of five consecutive odd numbers is 245. So, we can write this as: n + (n+2) + (n+4) + (n+6) + (n+8) = 245, where n is the smallest odd number.
-
Simplifying the equation, we get: 5n + 20 = 245.
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Solving for n, we get: n = (245 - 20) / 5 = 45. So, the smallest odd number is 45.
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The largest odd number would be n + 8 = 45 + 8 = 53.
-
The difference between twice the largest odd number and the smallest odd number is: 2*53 - 45 = 106 - 45 = 61.
So, the difference between twice the largest odd number and the smallest odd number is 61.
Solution 3
Sure, let's solve this step by step:
-
We know that the sum of five consecutive odd numbers is 245. So, we can write this as: n + (n+2) + (n+4) + (n+6) + (n+8) = 245, where n is the smallest odd number.
-
Simplifying the equation, we get: 5n + 20 = 245.
-
Solving for n, we subtract 20 from both sides: 5n = 225.
-
Then, we divide both sides by 5: n = 45. So, the smallest odd number is 45.
-
The largest odd number would be n + 8 = 45 + 8 = 53.
-
The difference between twice the largest odd number and the smallest odd number is: 2*53 - 45 = 106 - 45 = 61.
So, the difference is 61.
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