Five-ninths of number is equal to twenty five percent of the second number . The second number is equal to one-fourth of the third number. The value of the third number is 2960. What is 30 percent of the first number .

Options

A. 88.8
B. 99.9
C. 66.6
D. Cannot be determined

Explanation

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

**Step 1: Find the second number.**
We are told that the second number is equal to one-fourth of the third number. The value of the third number is given as 2960.

\[ \text{Second Number} = \frac{1}{4} \times \text{Third Number} = \frac{1}{4} \times 2960 \]

Calculating this:

\[ \text{Second Number} = \frac{2960}{4} = 740 \]

**Step 2: Set up the equation for the first number.**
We know that five-ninths of the first number is equal to twenty-five percent of the second number.

Let the first number be \( x \).

\[ \frac{5}{9}x = 25\% \text{ of Second Number} \]

Calculating 25% of the second number:

\[ 25\% \text{ of } 740 = \frac{25}{100} \times 740 = \frac{1}{4} \times 740 = 185 \]

Now we can set up the equation:

\[ \frac{5}{9}x = 185 \]

**Step 3: Solve for the first number \( x \).**
To isolate \( x \), we multiply both sides by \( \frac{9}{5} \):

\[ x = 185 \times \frac{9}{5} \]

Calculating this:

\[ x = 185 \times 1.8 = 333 \]

**Step 4: Find 30% of the first number.**
Now we need to calculate 30% of \( x \):

\[ 30\% \text{ of } x = \frac{30}{100} \times 333 = 0.3 \times 333 \]

Calculating this:

\[ 0.3 \times 333 = 99.9 \]

Thus, the final answer is:

\[ \text{30% of the first number is } 99.9 \]

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