Let's denote the number of months it will take Sonny to collect enough gems as \( x \).
Currently, Sonny has 76 gems and collects 4 gems per month. Therefore, the total number of gems Sonny will have after \( x \) months can be expressed as:
\[ 76 + 4x \]
Sonny wants to reach a total of 100 gems, so we can set up the equation:
\[ 76 + 4x = 100 \]
Now, we will solve for \( x \):
- Subtract 76 from both sides of the equation:
\[ 4x = 100 - 76 \]
\[ 4x = 24 \]
- Divide both sides by 4:
\[ x = \frac{24}{4} \]
\[ x = 6 \]
So, the equation is \( 76 + 4x = 100 \) and it will take Sonny 6 months to collect enough gems to reach his goal of 100 gems.