4. Two classes are planting trees. Class one plants 3 trees per person, and class two plants 5 trees per person, together planting a total of 115 trees. The maximum sum of the number of people in the two classes is $\qquad$ .
【Key Points】Combinations, Maximum Value Problems
【Difficulty】ふ
【Answer】 37 people.
【Analysis】Let class one have $a$ people, and class two have $b$ people, then we have $3 a+5 b=115$. To find the maximum number of people in both classes, the equation can be transformed into: $3(a+b)+2 b=115$, maximizing $a+b$ while minimizing $b$. When $b=2$, $a+b=37$. The maximum total number of people in both classes is 37.