Three consecutive odd numbers have a sum of 75. What is the greatest number?

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Three consecutive odd numbers have a sum of 75. What is the greatest number?

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Answer 1 · 2016-11-27T15:22:49

26

Explanation:

Let the three consecutive nos are $(x - 1)$ $(x-1)$ , $(x)$ $(x)$ & $(x + 1)$ $(x+1)$ .

As per question,

$(x - 1) + (x) + (x + 1)$ $(x-1) + (x) + (x+1)$ = 75

$3 x$ $3x$ = 75

$x = \frac{75}{3} = 25$ $x = 75/3 = 25$

Therefore the largest no = $x + 1$ $x+1$ = 25 + 1 = 26

Answer 2 · 2016-11-27T15:23:34

The largest or greatest number is 27.

The other two numbers are 23 and 25.

Explanation:

Let's call the largest odd number $x$ $x$ because this is what we are solving for.

If $x$ $x$ is the largest odd number and these are consecutive odd numbers we must subtract $2$ $2$ and $4$ $4$ from $x$ $x$ to get all three consecutive odd numbers.

So, the three consecutive odd numbers are: $x - 4$ $x - 4$ , $x - 2$ $x - 2$ and $x$ $x$ .

We know their sum, or adding them together, is $75$ $75$ so we can write and solve for $x$ $x$ :

$(x - 4) + (x - 2) + x = 75$ $(x - 4) + (x - 2) + x = 75$

$x - 4 + x - 2 + x = 75$ $x - 4 + x - 2 + x = 75$

$x + x + x - 4 - 2 = 75$ $x + x + x - 4 - 2 = 75$

$3 x - 6 = 75$ $3x - 6 = 75$

$3 x - 6 + 6 = 75 + 6$ $3x - 6 + 6 = 75 + 6$

$3 x = 81$ $3x = 81$

(3x)/3 = 81/3#

$x = 27$ $x = 27$

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Three consecutive odd numbers have a sum of 75. What is the greatest number?

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