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.

Equation
A) 4m = 100
B) 76m + 4 = 100
C) 100 + 4m = 76
D) 76 + 4m = 100
Time it will take
A) 6 months
B) 76 months
C) 25 months
D) 4 months

1 answer

To determine how long it will take Sonny to collect enough gems, we can represent the situation with the equation that incorporates his current gems and the gems he will collect over time.

Sonny currently has 76 gems and wants to reach a total of 100 gems. He collects 4 additional gems each month. The appropriate equation that represents this situation is:

\[ 76 + 4m = 100 \]

where \( m \) is the number of months.

Now, let's solve for \( m \):

  1. Start with the equation: \[ 76 + 4m = 100 \]

  2. Subtract 76 from both sides: \[ 4m = 100 - 76 \]

  3. Simplify the right side: \[ 4m = 24 \]

  4. Now, divide both sides by 4: \[ m = 6 \]

Thus, the solution to the equation is \( m = 6 \).

Equation: D) \( 76 + 4m = 100 \)
Time it will take: A) 6 months