Questions: 10/(a-6) = 5/6

10/(a-6) = 5/6
Transcript text: $\frac{10}{a-6}=\frac{5}{6}$
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Solution

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Solution Steps

To solve the equation \(\frac{10}{a-6}=\frac{5}{6}\), we can use cross-multiplication to eliminate the fractions. This will give us a linear equation in terms of \(a\). We then solve for \(a\) by isolating it on one side of the equation.

Step 1: Cross-Multiply

Starting with the equation

\[ \frac{10}{a-6} = \frac{5}{6} \]

we can cross-multiply to eliminate the fractions:

\[ 10 \cdot 6 = 5 \cdot (a - 6) \]

This simplifies to:

\[ 60 = 5(a - 6) \]

Step 2: Distribute and Rearrange

Next, we distribute the \(5\) on the right side:

\[ 60 = 5a - 30 \]

Now, we add \(30\) to both sides to isolate the term with \(a\):

\[ 60 + 30 = 5a \]

This simplifies to:

\[ 90 = 5a \]

Step 3: Solve for \(a\)

Finally, we divide both sides by \(5\) to solve for \(a\):

\[ a = \frac{90}{5} = 18 \]

Final Answer

\(\boxed{a = 18}\)

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