Answer :

To solve the equation [tex]\(\frac{1}{2} a + \frac{1}{4} a + \frac{1}{8} a + 25 = a\)[/tex], let's proceed step-by-step.

1. Combine the terms involving [tex]\(a\)[/tex] on the left side of the equation:
[tex]\[ \frac{1}{2}a + \frac{1}{4}a + \frac{1}{8}a + 25 = a \][/tex]

2. Find a common denominator for the fractions [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{1}{4}\)[/tex], and [tex]\(\frac{1}{8}\)[/tex]. The common denominator is 8.

[tex]\[ \frac{1}{2}a = \frac{4}{8}a \][/tex]
[tex]\[ \frac{1}{4}a = \frac{2}{8}a \][/tex]
[tex]\[ \frac{1}{8}a = \frac{1}{8}a \][/tex]

3. Now add these fractions:
[tex]\[ \frac{4}{8}a + \frac{2}{8}a + \frac{1}{8}a = \frac{7}{8}a \][/tex]

So the equation becomes:
[tex]\[ \frac{7}{8}a + 25 = a \][/tex]

4. Isolate the term involving [tex]\(a\)[/tex] on the left side by subtracting [tex]\(\frac{7}{8}a\)[/tex] from both sides of the equation:
[tex]\[ \frac{7}{8}a + 25 - \frac{7}{8}a = a - \frac{7}{8}a \][/tex]

Simplifying, we get:
[tex]\[ 25 = a - \frac{7}{8}a \][/tex]

5. Combine the [tex]\(a\)[/tex] terms on the right side:
[tex]\[ 25 = \frac{8}{8}a - \frac{7}{8}a \][/tex]

Simplifying:
[tex]\[ 25 = \frac{1}{8}a \][/tex]

6. Solve for [tex]\(a\)[/tex] by multiplying both sides of the equation by 8:
[tex]\[ 25 \times 8 = a \][/tex]

[tex]\[ 200 = a \][/tex]

Thus, the solution to the equation [tex]\(\frac{1}{2}a + \frac{1}{4}a + \frac{1}{8}a + 25 = a\)[/tex] is:
[tex]\[ a = 200 \][/tex]