If a is 63% of x and c is `(3)/(8)` of x, which of the following is the closest to the ratio of a to c?

Options

A. `0.236`
B. `0.381`
C. `0.595`
D. `1.680`

Answer

To find the ratio of \( a \) to \( c \) given that \( a \) is 63% of \( x \) and \( c \) is \( \frac{3}{8} \) of \( x \), we can follow these steps:

### Step 1: Express \( a \) and \( c \) in terms of \( x \)
- Since \( a \) is 63% of \( x \), we can write:
\[ a = 0.63x \]
- Since \( c \) is \( \frac{3}{8} \) of \( x \), we can write:
\[ c = \frac{3}{8}x \]

### Step 2: Set up the ratio \( \frac{a}{c} \)
- Now, we want to find the ratio of \( a \) to \( c \):
\[ \frac{a}{c} = \frac{0.63x}{\frac{3}{8}x} \]

### Step 3: Simplify the ratio
- The \( x \) in the numerator and denominator cancels out:
\[ \frac{a}{c} = \frac{0.63}{\frac{3}{8}} \]

### Step 4: Rewrite the division as multiplication
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{a}{c} = 0.63 \times \frac{8}{3} \]

### Step 5: Calculate the multiplication
- Now, we perform the multiplication:
\[ 0.63 \times \frac{8}{3} = \frac{0.63 \times 8}{3} = \frac{5.04}{3} \approx 1.68 \]

### Conclusion
- Therefore, the closest ratio of \( a \) to \( c \) is approximately \( 1.68 \).

### Final Answer
- The option that is closest to this value is \( d \).