If (x+2):3=(x+5): 4, what is the value of x?

If (x+2):3=(x+5): 4, what is the value of x? ?

Created: 1 year ago | Updated: 2 months ago | Created By:

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Institution: Bank Asia Ltd Exam: Bank Asia Ltd - Management Trainee Officer - 22.05.2015 ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the proportion \((x+2):3=(x+5):4\), we can start by cross-multiplying. This means we multiply the outer terms and the inner terms:

\[
(x + 2) \cdot 4 = (x + 5) \cdot 3
\]

Expanding both sides gives us:

\[
4x + 8 = 3x + 15
\]

Next, we want to isolate \(x\). To do this, we can subtract \(3x\) from both sides:

\[
4x - 3x + 8 = 15
\]

This simplifies to:

\[
x + 8 = 15
\]

Now, to solve for \(x\), we subtract 8 from both sides:

\[
x = 15 - 8
\]
\[
x = 7
\]

Thus, the solution to the equation is \(x = 7\).

To verify, we can substitute \(x = 7\) back into the original proportion:

For the left side:
\[
(7 + 2) : 3 = 9 : 3 = 3
\]

For the right side:
\[
(7 + 5) : 4 = 12 : 4 = 3
\]

Both sides are equal, confirming that our solution is correct. Therefore, the value of \(x\) is indeed **7,** making option A the correct choice.

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