Question

Which equation is equivalent to –k + 0.03 + 1.01k = –2.45 – 1.81k?

–100k + 3 + 101k = –245 – 181k
–100k + 300 + 101k = –245 – 181k
–k + 3 + 101k = –245 – 181k
–k + 300 + 101k = –245 – 181k

Answer 1

To find the equivalent equation, we will first manipulate the original equation

\[
-k + 0.03 + 1.01k = -2.45 - 1.81k.
\]

1. First, let's combine like terms on the left side:
\[
-k + 1.01k = 0.01k.
\]
So, the left side becomes:
\[
0.01k + 0.03.
\]

2. Now, let's rewrite the equation:
\[
0.01k + 0.03 = -2.45 - 1.81k.
\]

3. Next, we can express the constants on the right side in a nicer form:
\[
0.01k + 0.03 = -2.45 - 1.81k.
\]

4. To eliminate decimals, we can multiply the entire equation by 100:
\[
100(0.01k) + 100(0.03) = 100(-2.45) + 100(-1.81k).
\]
This yields:
\[
k + 3 = -245 - 181k.
\]

5. Rearranging gives us:
\[
k + 181k + 3 = -245,
\]
which simplifies to:
\[
182k + 3 = -245.
\]

Now let’s analyze the options provided.

1. **First option:** \(-100k + 3 + 101k = -245 - 181k\) simplifies to \(k + 3 = -245 - 181k\), which follows the equation we derived, so this is **True**.

2. **Second option:** \(-100k + 300 + 101k = -245 - 181k\) gives us \(k + 300 = -245 - 181k\), which doesn't work with our simplified equation so **False**.

3. **Third option:** \(-k + 3 + 101k = -245 - 181k\) gives us \(100k + 3 = -245 - 181k\), which is also not the same as our equation so **False**.

4. **Fourth option:** \(-k + 300 + 101k = -245 - 181k\) gives us \(100k + 300 = -245 - 181k\) and also doesn't match **False**.

Thus, the correct equivalent equation is:

\(-100k + 3 + 101k = -245 - 181k\).