35 % of a number is two times 75 % of another number. What is the ratio between the first and the second number , respetively ?

Options

A. `35 : 6`
B. `31 : 7`
C. `23 : 7`
D. None of the above

Answer

Let's denote the first number as \( x \) and the second number as \( y \).

### Step 1: Set up the equation based on the problem statement
According to the problem, we have:
\[ 35\% \text{ of } x = 2 \times (75\% \text{ of } y) \]

### Step 2: Convert percentages to fractions
We can convert the percentages to fractions:
\[ 35\% = \frac{35}{100} = \frac{7}{20} \]
\[ 75\% = \frac{75}{100} = \frac{3}{4} \]

### Step 3: Substitute the fractions into the equation
Now we can substitute these fractions into our equation:
\[ \frac{7}{20} x = 2 \times \left(\frac{3}{4} y\right) \]

### Step 4: Simplify the right-hand side
Calculating the right-hand side:
\[ 2 \times \frac{3}{4} y = \frac{6}{4} y = \frac{3}{2} y \]
So now our equation looks like:
\[ \frac{7}{20} x = \frac{3}{2} y \]

### Step 5: Cross-multiply to eliminate the fractions
To eliminate the fractions, we can cross-multiply:
\[ 7x \cdot 2 = 3y \cdot 20 \]
This simplifies to:
\[ 14x = 60y \]

### Step 6: Rearrange to find the ratio of \( x \) to \( y \)
Now we can rearrange this equation to find the ratio:
\[ \frac{x}{y} = \frac{60}{14} \]

### Step 7: Simplify the ratio
Now we simplify \( \frac{60}{14} \):
\[ \frac{60}{14} = \frac{30}{7} \]

### Final Answer
Thus, the ratio between the first number \( x \) and the second number \( y \) is:
\[ \boxed{30:7} \]

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