For solving the equation, suppose there are X people in mathematics, Y people in science and technology, and S people in total.

S =(x+y)- 12- There are 12 people in both interest groups.

X = 3 * s/5-the number of people in the math group accounts for three-fifths of the total number of people in the two groups.

Y = 4 * s/7-the number of people in the science and technology group accounts for four-sevenths of the total number of people in the two groups.

X=42, y=40 and s=70 are obtained by joint solution.