Let's define the variables and write an equation to determine how long it will take Sonny to collect the additional gems he needs.
Sonny currently has 76 gems and wants to have a total of 100 gems. Thus, he needs to collect:
\[ 100 - 76 = 24 \text{ gems} \]
Sonny collects an additional 4 gems per month. We can denote the number of months Sonny needs to collect the additional gems as \(x\).
Now we can set up the equation:
\[ 4x = 24 \]
To find \(x\), divide both sides of the equation by 4:
\[ x = \frac{24}{4} = 6 \]
Thus, it will take Sonny 6 months to collect the additional 24 gems and reach a total of 100 gems.
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