If `x:y=2:5`, then `(10x+3y):(5x+2y)` is ________.

Answer

To solve the problem where \( x:y = 2:5 \) and we need to find \( (10x + 3y):(5x + 2y) \), we can follow these steps:

### Step 1: Express x and y in terms of a common variable
Since \( x:y = 2:5 \), we can express \( x \) and \( y \) as:
- Let \( x = 2a \)
- Let \( y = 5a \)

### Step 2: Substitute x and y into the expression
Now we substitute \( x \) and \( y \) into the expression \( (10x + 3y):(5x + 2y) \):
- \( 10x + 3y = 10(2a) + 3(5a) \)
- \( 5x + 2y = 5(2a) + 2(5a) \)

### Step 3: Simplify the expressions
Now we simplify both parts:
- For \( 10x + 3y \):
\[ 10(2a) + 3(5a) = 20a + 15a = 35a \]
- For \( 5x + 2y \):
\[ 5(2a) + 2(5a) = 10a + 10a = 20a \]

### Step 4: Write the ratio
Now we can write the ratio:
\[ (10x + 3y):(5x + 2y) = 35a : 20a \]

### Step 5: Simplify the ratio
Since \( a \) is common in both terms, we can cancel it out:
\[ 35a : 20a = 35 : 20 \]

### Step 6: Reduce the ratio to simplest form
To simplify \( 35 : 20 \), we divide both terms by their greatest common divisor, which is 5:
\[ \frac{35}{5} : \frac{20}{5} = 7 : 4 \]

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

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