The given equation can be expressed as:
\[ 5A - 10 = 10 \left( \frac{1}{4}A + 12 \right) \]
Now, let's solve for \( A \):
\[ 5A - 10 = \frac{10}{4}A + 120 \]
Combine like terms:
\[ 5A - \frac{5}{2}A = 130 \]
Multiply both sides by 2 to get rid of the fraction:
\[ 10A - 5A = 260 \]
Simplify:
\[ 5A = 260 \]
Now, divide by 5 to solve for \( A \):
\[ A = 52 \]
Therefore, the value of \( A \) (the number) is 52.