Question

Solve for
\[c\].
Give an exact answer.
\[0.2(10-5c)=5c-16\]
\[c =\]

Answer 1

We start with the equation:

\[
0.2(10 - 5c) = 5c - 16.
\]

First, we distribute \(0.2\) on the left side:

\[
0.2 \cdot 10 - 0.2 \cdot 5c = 5c - 16,
\]

which simplifies to:

\[
2 - c = 5c - 16.
\]

Next, we want to isolate \(c\). We can move \(c\) to the right side by adding \(c\) to both sides:

\[
2 = 5c + c - 16,
\]

which simplifies to:

\[
2 = 6c - 16.
\]

Now, we add \(16\) to both sides:

\[
2 + 16 = 6c,
\]

which gives us:

\[
18 = 6c.
\]

Now, we solve for \(c\) by dividing both sides by \(6\):

\[
c = \frac{18}{6} = 3.
\]

Thus, the exact answer is:

\[
\boxed{3}.
\]