Rationale
g + 100 equals 150.
To find the value of g + 100, we first determine g from the given average. The average of g and 100 is calculated as (g + 100) / 2 = 75. Multiplying both sides by 2 gives us g + 100 = 150.
A) This choice implies that g + 100 equals 50, which would suggest that g is negative (-50). However, this contradicts the average of 75 when calculated with 100, as the average would be significantly less than 75.
B) Selecting 125 for g + 100 would mean that g is 25. When calculating the average (25 + 100) / 2, the result is 62.5, which is much lower than the required average of 75, making this option incorrect.
C) This is the correct answer, as g + 100 equals 150. To confirm, substituting this into the average formula yields (g + 100) / 2 = 75, resulting in (150) / 2 = 75, which is accurate.
D) If g + 100 were 175, it would mean g is 75. The average calculation (75 + 100) / 2 results in 87.5, which is higher than the specified average of 75, thus making this choice incorrect.
Conclusion
In this problem, the calculation of the average led us directly to the conclusion that g + 100 equals 150. By determining g from the average equation, we confirmed that only option C aligns with the requirement of an average of 75. Other choices did not meet the condition, reinforcing the importance of accurate average calculations in solving for unknowns.