If 10% of x is 3 times 15% of y then find x: y.

Options

A. A) `7:2`
B. B) `9:2`
C. C) `8:3`
D. D) `11:4`

Answer

To solve the problem, we need to express the given information mathematically and then simplify it to find the ratio \( x : y \).

### Step-by-Step Solution:

1. **Translate the Problem into an Equation:**
The problem states that 10% of \( x \) is equal to 3 times 15% of \( y \). We can write this as:
\[ 0.1x = 3 \times 0.15y \]

2. **Simplify the Right Side:**
Calculate \( 3 \times 0.15 \):
\[ 3 \times 0.15 = 0.45 \]
Now, we can rewrite the equation:
\[ 0.1x = 0.45y \]

3. **Isolate \( x \) in Terms of \( y \):**
To find \( x \) in terms of \( y \), divide both sides of the equation by 0.1:
\[ x = \frac{0.45y}{0.1} \]

4. **Calculate the Division:**
Now, calculate \( \frac{0.45}{0.1} \):
\[ \frac{0.45}{0.1} = 4.5 \]
Therefore, we have:
\[ x = 4.5y \]

5. **Express the Ratio \( x : y \):**
Now, we can express the ratio \( x : y \):
\[ x : y = 4.5 : 1 \]

6. **Convert to Fraction:**
To express this ratio in a simpler form, we can multiply both parts by 2 to eliminate the decimal:
\[ x : y = 9 : 2 \]

### Final Answer:
Thus, the ratio \( x : y \) is \( 9 : 2 \).

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