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Q13. The sum of three consecutive integers is 30. Which of the following is the largest among the three?

Q. 13. तीन लगातार पूर्णांकों का योग 30 है। निम्नलिखित में से कौन सा तीनों में सबसे बड़ा है?

Sagot :

GinnyAnsweridn
To find the largest among three consecutive integers whose sum is 30, follow these steps:

1. Consider Three Consecutive Integers:
Let the three consecutive integers be [tex]\( x \)[/tex], [tex]\( x + 1 \)[/tex], and [tex]\( x + 2 \)[/tex].

2. Set Up the Equation:
The sum of these three integers is given as 30. Therefore, we can write the equation:
[tex]\[ x + (x + 1) + (x + 2) = 30 \][/tex]

3. Combine Like Terms:
Simplify the equation by combining like terms:
[tex]\[ x + x + 1 + x + 2 = 30 \][/tex]
[tex]\[ 3x + 3 = 30 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
First, subtract 3 from both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 3x + 3 - 3 = 30 - 3 \][/tex]
[tex]\[ 3x = 27 \][/tex]
Next, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 9 \][/tex]

5. Identify the Three Consecutive Integers:
If [tex]\( x \)[/tex] is 9, then the three consecutive integers are:
[tex]\[ x = 9 \][/tex]
[tex]\[ x + 1 = 10 \][/tex]
[tex]\[ x + 2 = 11 \][/tex]

6. Determine the Largest Integer:
Among the integers 9, 10, and 11, the largest is 11.

Therefore, the largest among the three consecutive integers whose sum is 30 is [tex]\( 11 \)[/tex].
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