If `(18)/(r+10)=(3)/(r)`, what is the value of `(r)/(3)`?

Options

A. `(2)/(3)`
B. `(3)/(2)`
C. `2`
D. `3`

Answer

To solve the equation \(\frac{18}{r+10} = \frac{3}{r}\) and find the value of \(\frac{r}{3}\), we can follow these steps:

### Step 1: Cross-Multiply
We start with the equation:
\[ \frac{18}{r+10} = \frac{3}{r} \]
Cross-multiplying gives us:
\[ 18 \cdot r = 3 \cdot (r + 10) \]

### Step 2: Distribute on the Right Side
Now, we distribute \(3\) on the right side:
\[ 18r = 3r + 30 \]

### Step 3: Rearrange the Equation
Next, we rearrange the equation to isolate \(r\):
\[ 18r - 3r = 30 \]
This simplifies to:
\[ 15r = 30 \]

### Step 4: Solve for \(r\)
Now, we divide both sides by \(15\) to solve for \(r\):
\[ r = \frac{30}{15} = 2 \]

### Step 5: Find \(\frac{r}{3}\)
Finally, we need to find \(\frac{r}{3}\):
\[ \frac{r}{3} = \frac{2}{3} \]

Thus, the value of \(\frac{r}{3}\) is \(\frac{2}{3}\).

### Final Answer
\(\frac{r}{3} = \frac{2}{3}\)

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