Maths Olympiad Prep

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Algebra Difficulty 5.6 AIME, harder Find the answer

9. There are 20 people, including college students, middle school students, and primary school students, going to the park. The entrance fee for college students is 3 yuan per person, for middle school students 2 yuan per person, and for primary school students 50 cents per person. It is known that the total entrance fee is 20 yuan. How many college, middle school, and primary school students are there?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

9. x,y,zx, y, z represent the number of high school, middle school, and elementary school students respectively. x+y+z=20,6x+4y+z=40x+y+z=20, 6x+4y+z=40. x=4,y=0,z=16;x=1,y=5,z=14x=4, y=0, z=16 ; x=1, y=5, z=14.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.