Four positive integers have average 73.5. The highest is 108 and the lowest is 29. The remaining two differ by 15. Find the smaller of those two remaining integers.

Introduction / Context:This question combines an average-to-total conversion with constraints on two unknown integers. Setting variables for the two middle integers converts the text into a simple linear equation.

Given Data / Assumptions:

• Average of 4 integers = 73.5
• Highest = 108
• Lowest = 29
• Difference between the remaining two = 15

Concept / Approach:Let the remaining two numbers be x and x + 15. Use the total from the average and subtract the known extremes to isolate x.

Step-by-Step Solution:

Verification / Alternative check:Numbers are 29, 71, 86, 108. Average = (29 + 71 + 86 + 108) / 4 = 294 / 4 = 73.5; difference between middle pair = 15, all conditions met.

Why Other Options Are Wrong:

• 73, 80, 86: do not satisfy the total and the exact difference simultaneously.
• Cannot be determined: the information is sufficient to solve uniquely.

Common Pitfalls:Forgetting to include the +15 when forming the equation for the two unknowns or miscalculating the total from the average.

Final Answer:71