We are given the equation $7 - \frac{k}{4} = \frac{k}{10}$ and asked to solve for the variable $k$.

1. Problem Description

We are given the equation $7 - \frac{k}{4} = \frac{k}{10}$ and asked to solve for the variable $k$.

2. Solution Steps

First, we want to isolate the terms with $k$ on one side of the equation. Add $\frac{k}{4}$ to both sides of the equation:

$7 - \frac{k}{4} + \frac{k}{4} = \frac{k}{10} + \frac{k}{4}$

$7 = \frac{k}{10} + \frac{k}{4}$

Next, we need to find a common denominator for the fractions $\frac{k}{10}$ and $\frac{k}{4}$. The least common multiple of 10 and 4 is

2

0. So, we rewrite the fractions with a denominator of 20:

$\frac{k}{10} = \frac{2k}{20}$

$\frac{k}{4} = \frac{5k}{20}$

Now substitute these into the equation:

$7 = \frac{2k}{20} + \frac{5k}{20}$

$7 = \frac{2k + 5k}{20}$

$7 = \frac{7k}{20}$

To solve for $k$, we can multiply both sides of the equation by 20:

$7 \cdot 20 = \frac{7k}{20} \cdot 20$

$140 = 7k$

Finally, divide both sides by 7 to isolate $k$:

$\frac{140}{7} = \frac{7k}{7}$

$20 = k$

So, $k = 20$.

3. Final Answer

The final answer is $k = 20$.