Mathematical Olympiad problem of one variable linear equation to be solved in detail A middle school enrolled 750 students last year. This year, the number of boys increased by one sixth and the number of girls decreased by one fifth. This year, 710 students were enrolled. How many boys and girls are enrolled this year?

Setting: this year, there are (x + 1 / 6x) male students and (750-x) × (1-1 / 5) female students
(X+1/6X)+(750-X)×（1-1/5）=710 7/6X+(750-X)4/5=710
7 / 6x + 600-4 / 5x = 710 multiply both sides by 30 to get 35x + 18000-24x = 21300
11X=3300 X=300
300 + 300 × 1 / 6 = 300 + 50 = 350 (male) (750-300) - (750-300) × 1 / 5 = 450-90 = 360 (female)
A: there are 350 boys and 360 girls enrolled this year

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