The average of four positive integers is 59. The highest integer is 83, and the lowest integer is 29. The difference between the remaining two integers is 28. Determine the higher of the remaining two integers.

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Accepted Answer

Calculate the total sum of the four integers:  
   $$
   	ext{Total sum} = 	ext{Average} 	imes 	ext{Number of integers} = 59 	imes 4 = 236.
   $$

Subtract the highest and lowest integers from the total sum to find the sum of the remaining two integers:  
   $$
   	ext{Remaining sum} = 236 - (83 + 29) = 236 - 112 = 124.
   $$

Let the two remaining integers be $$ x $$ and $$ x - 28 $$ (since their difference is given as 28). Solve for $$ x $$:  
   $$
   x + (x - 28) = 124
   $$  
   Simplify:  
   $$
   2x - 28 = 124
   $$  
   $$
   2x = 152 \quad \Rightarrow \quad x = 76.
   $$

Thus, the higher of the two remaining integers is **76**.

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