Two-third of the first number is equal to the cube of the second number. If the second number is equal to twelve percent of 50. What is the sum of the first and the second numbers ?

Options

A. 330
B. 360
C. 390
D. 372

Answer

To solve the problem step by step, we will follow the instructions given in the question.

### Step 1: Determine the second number
The second number (let's call it B) is given as 12% of 50.

To calculate this:
\[ B = \frac{12}{100} \times 50 \]

Calculating this gives:
\[ B = 0.12 \times 50 = 6 \]

### Step 2: Set up the equation for the first number
According to the question, two-thirds of the first number (let's call it A) is equal to the cube of the second number (B).

This can be expressed as:
\[ \frac{2}{3} A = B^3 \]

Substituting the value of B we found:
\[ \frac{2}{3} A = 6^3 \]

Calculating \(6^3\):
\[ 6^3 = 216 \]

So the equation now is:
\[ \frac{2}{3} A = 216 \]

### Step 3: Solve for the first number (A)
To find A, we can multiply both sides of the equation by \(\frac{3}{2}\):
\[ A = 216 \times \frac{3}{2} \]

Calculating this gives:
\[ A = 216 \times 1.5 = 324 \]

### Step 4: Find the sum of the first and second numbers
Now that we have both numbers, we can find their sum:
\[ A + B = 324 + 6 \]

Calculating this gives:
\[ A + B = 330 \]

### Final Answer
The sum of the first and second numbers is:
\[ \boxed{330} \]