If `(2)/(3) x = 0.6 and 0.02 y =1`, then the value of `x +y^(-1)` is

Options

A. `0.92`
B. `1.1`
C. `49.1`
D. `50.9`

Answer

To solve the problem, we need to find the value of \( x + y^{-1} \) given the equations \( \frac{2}{3} x = 0.6 \) and \( 0.02 y = 1 \).

### Step-by-Step Solution:

1. **Solve for \( x \)**:
\[ \frac{2}{3} x = 0.6 \]
To isolate \( x \), multiply both sides by \( \frac{3}{2} \):
\[ x = 0.6 \times \frac{3}{2} \]
Calculate \( 0.6 \times 3 = 1.8 \):
\[ x = \frac{1.8}{2} = 0.9 \]

2. **Solve for \( y \)**:
\[ 0.02 y = 1 \]
To isolate \( y \), divide both sides by \( 0.02 \):
\[ y = \frac{1}{0.02} \]
Calculate \( \frac{1}{0.02} = 50 \):
\[ y = 50 \]

3. **Find \( y^{-1} \)**:
\[ y^{-1} = \frac{1}{y} = \frac{1}{50} = 0.02 \]

4. **Calculate \( x + y^{-1} \)**:
\[ x + y^{-1} = 0.9 + 0.02 \]
Add the two values:
\[ x + y^{-1} = 0.92 \]

### Final Answer:
\[ x + y^{-1} = 0.92 \]