Question 1180494: in yoga class, all of the students are lined up according to height. Andy notices that the number of students who are taller than he is one-fourth the number of students who are shorter than he. Violetta notices that there are 3 times as many students who are taller than she than students who are shorter than she. How many students are the class is there are fewer than 40 students?
Answer by ikleyn(52793)   (Show Source):
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in yoga class, all of the students are lined up according to height.
Andy notices that the number of students who are taller than he is one-fourth the number of students who are shorter than he.
Violetta notices that there are 3 times as many students who are taller than she than students who are shorter than she.
How many students are the class is there are fewer than 40 students?
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First, consider Andy.
Let x be the number of students who are taller than he.
Then the number of the rest students, excluding him, is 4x, according to the condition.
So, the total number of students in the class is (x + 4x + 1), or 5x+1.
Next, consider Violette.
Let y be the number of students who are shorter than she.
Then the number of the rest students, excluding her, is 3y, according to the condition.
So, the total number of students in the class is (y + 3y + 1), or 4y+1.
We see, that the number of students in the class MINUS one is a multiple of 4 (four) and of 5 (five), at the same time.
So, the number of students in the class is EITHER 20+1 = 21 OR 40+1 = 41, if consider couple of minimal values.
But 41 is excluded by the condition, leaving a UNIQUE ANSWER:
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| The number of students in the class is 21. |
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Solved.
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