1. **State the problem:** The MTAP Club started with an initial number of members in June. Each month, every member recruited exactly two new members. By August, the club had 124 members. We need to find the initial number of members in June. 2. **Understand the growth pattern:** Each member recruits 2 new members every month. This means the number of members triples each month (the original members plus twice their number as new members). 3. **Define variables:** Let $x$ be the initial number of members in June. 4. **Write the formula for growth:** After one month (July), the number of members is $3x$. After two months (August), the number of members is $3 \times 3x = 3^2 x = 9x$. 5. **Use the given data:** We know that in August, the number of members is 124, so: $$9x = 124$$ 6. **Solve for $x$:** $$x = \frac{124}{9}$$ 7. **Simplify the fraction:** $$x = \frac{\cancel{124}}{\cancel{9}}$$ Since 124 and 9 have no common factors, the fraction remains $\frac{124}{9} \approx 13.78$. 8. **Interpret the result:** Since the number of members must be a whole number, and the growth is exact, we check if the problem expects an integer. The closest integer is 14, but let's verify: If $x=14$, then August members = $9 \times 14 = 126$ (too high). If $x=13$, then August members = $9 \times 13 = 117$ (too low). Since the problem states exactly 124 members, the initial number of members is $\frac{124}{9}$, which is approximately 13.78. **Final answer:** The initial number of members in June was $\boxed{\frac{124}{9}}$ or approximately 13.78 members. Since the number of members must be whole, the problem might have rounding or estimation involved, but mathematically, the exact initial number is $\frac{124}{9}$.