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.

Question

Write an equation and solve for the number of months it will take Sonny to collect 100 gems.

Equation:

Time it will take:

Answer 1

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 \( x \):

1. Subtract 76 from both sides of the equation:

\[ 4x = 100 - 76 \]

\[ 4x = 24 \]

2. 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.