If `3/4` of a number is 7 more than `1/6` of the number, then `5/3` of the number is :

Options

A. 12
B. 20
C. 15
D. 18

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Set up the equation based on the problem statement.
According to the question, \( \frac{3}{4} \) of the number \( x \) is 7 more than \( \frac{1}{6} \) of the number \( x \). We can express this relationship mathematically as:

\[ \frac{3}{4}x = \frac{1}{6}x + 7 \]

### Step 2: Eliminate the fractions.
To eliminate the fractions, we can find a common denominator. The least common multiple (LCM) of 4 and 6 is 12. We will multiply every term in the equation by 12:

\[ 12 \left(\frac{3}{4}x\right) = 12 \left(\frac{1}{6}x\right) + 12 \cdot 7 \]

This simplifies to:

\[ 9x = 2x + 84 \]

### Step 3: Rearrange the equation.
Next, we will rearrange the equation to isolate \( x \):

\[ 9x - 2x = 84 \]

This simplifies to:

\[ 7x = 84 \]

### Step 4: Solve for \( x \).
Now, we can solve for \( x \) by dividing both sides of the equation by 7:

\[ x = \frac{84}{7} \]

Calculating this gives:

\[ x = 12 \]

### Step 5: Find \( \frac{5}{3} \) of the number.
Now that we have the value of \( x \), we need to find \( \frac{5}{3} \) of \( x \):

\[ \frac{5}{3}x = \frac{5}{3} \cdot 12 \]

Calculating this gives:

\[ \frac{5 \cdot 12}{3} = \frac{60}{3} = 20 \]

### Final Answer:
Thus, \( \frac{5}{3} \) of the number is \( 20 \).

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