if `x:y=2:5` then `(10x+3y):(5x+2y)` is _____.

Answer

To solve the problem, we need to find the ratio \((10x + 3y):(5x + 2y)\) given that \(x:y = 2:5\).

### Step-by-Step Solution:

1. **Express x in terms of y**:
Since \(x:y = 2:5\), we can express \(x\) in terms of \(y\):
\[ x = \frac{2}{5}y \]

2. **Substitute x in the expression**:
Now, substitute \(x\) in the expression \(10x + 3y\) and \(5x + 2y\):
\[ 10x + 3y = 10\left(\frac{2}{5}y\right) + 3y = 4y + 3y = 7y \]
\[ 5x + 2y = 5\left(\frac{2}{5}y\right) + 2y = 2y + 2y = 4y \]

3. **Form the ratio**:
Now we can form the ratio:
\[ (10x + 3y):(5x + 2y) = 7y:4y \]

4. **Simplify the ratio**:
Since \(y\) is common in both terms, we can cancel \(y\):
\[ 7y:4y = 7:4 \]

### Final Answer:
Thus, \((10x + 3y):(5x + 2y)\) is \(7:4\).

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