যদি x+y=6, y+z=7 এবং z+x=9 হয়, তাহলে x,y ও z গড় মান কত?

যদি x+y=6, y+z=7 এবং z+x=9 হয়, তাহলে x,y ও z গড় মান কত? ?

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Institution: জগন্নাথ বিশ্ববিদ্যালয় Exam: C ইউনিট : 2017-2018
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we have the following equations:

1. \( x + y = 6 \)
2. \( y + z = 7 \)
3. \( z + x = 9 \)

We need to find the individual values of \( x \), \( y \), and \( z \) in order to compute their average.

First, we can add all three equations together:

\[
(x + y) + (y + z) + (z + x) = 6 + 7 + 9
\]

This simplifies to:

\[
2x + 2y + 2z = 22
\]

Dividing the entire equation by 2 gives:

\[
x + y + z = 11
\]

Now, the average of \( x \), \( y \), and \( z \) is calculated by dividing the sum of the variables by 3:

\[
\text{Average} = \frac{x + y + z}{3} = \frac{11}{3}
\]

Thus, the average of \( x \), \( y \), and \( z \) is \( \frac{11}{3} \). All options were carefully reviewed, confirming that the correct answer is indeed \( \frac{11}{3} \), which corresponds to choices A and B. Therefore, the final answer is \( \frac{11}{3} \).

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