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Question
300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.
Solution
Let the total number of students be x. According to the question:
`300/x-300/(x+10)=1`
⇒`(300(x+10)-300x)/(x(x+10))=1`
⇒`(300x+3000-300x)/(x^2+10x)=1`
⇒`3000=x^2+10x`
⇒`x^2+10x-3000=0`
⇒`x^2+(60-50)x=3000=0`
⇒`x^2+60x-50x-3000=0`
⇒`x(x+60)-50(x+60)=0`
⇒`(x+60)(x-50)=0`
⇒`x=50 or x=-60`
x cannot be negative; therefore, the total number of students is 50.
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