Question

2/3(6k-30)+k=100 with work shown

Answer 1

To solve the equation \( \frac{2}{3}(6k - 30) + k = 100 \), we will follow these steps:

### Step 1: Distribute \( \frac{2}{3} \)
First, distribute \( \frac{2}{3} \) across the parentheses.

\[
\frac{2}{3} \times 6k - \frac{2}{3} \times 30
\]

Calculating each part:

1. \( \frac{2}{3} \times 6k = \frac{12k}{3} = 4k \)
2. \( \frac{2}{3} \times 30 = \frac{60}{3} = 20 \)

Now, substituting these back into the equation:

\[
4k - 20 + k = 100
\]

### Step 2: Combine like terms
Combine the terms involving \( k \):

\[
4k + k - 20 = 100
\]
This simplifies to:

\[
5k - 20 = 100
\]

### Step 3: Add 20 to both sides
To isolate the term with \( k \), add 20 to both sides of the equation:

\[
5k - 20 + 20 = 100 + 20
\]

This simplifies to:

\[
5k = 120
\]

### Step 4: Divide by 5
Now, divide both sides by 5 to solve for \( k \):

\[
k = \frac{120}{5} = 24
\]

### Conclusion
The solution to the equation \( \frac{2}{3}(6k - 30) + k = 100 \) is:

\[
k = 24
\]