Question

Sonny is collecting rare gems to add to his large collection. Sonny currently has 76 gems and would like to get to 100 gems by collecting an additional 4 gems per month. Write an equation and solve for the number of months it will take Sonny to collect 100 gems.

Answer 1

To determine the number of months it will take Sonny to collect 100 gems, we can start by defining the variable \( x \) as the number of months Sonny will collect gems.

Currently, Sonny has 76 gems, and he collects 4 gems per month. We can write the equation based on this information:

\[
76 + 4x = 100
\]

Now, we can solve for \( x \):

1. Subtract 76 from both sides:
\[
4x = 100 - 76
\]
\[
4x = 24
\]

2. Divide both sides by 4:
\[
x = \frac{24}{4}
\]
\[
x = 6
\]

So, it will take Sonny **6 months** to collect enough gems to reach a total of 100 gems.