A certain number of students, X boys and 14girls,went camping. After 3 days,19 of them left. The total number of students that remained still exceeded 3/5 of the original number of students. Find the value of X.
要用Linear Inequalities in One Unknown
最好條式 有埋解釋
THX
F.3 Maths 1題
2008-11-12 5:30 am
回答 (2)
2008-11-12 5:47 am
✔ 最佳答案
Original number of students = X + 14.When 19 left, number remaining = X + 14 - 19 = X - 5.
So X-5 > 3(X + 14)/5
5X - 25 > 3X + 42
2X > 67
X > 33.5
Therefore, X is greater than or equal to 34.
2008-11-12 6:24 am
(X + 14) x 2/5 > 19
since remained students more than 3/5 of original (X + 14), so 19 of them must less than 2/5 of original.
(X + 14) > 19 x 5/2
X > 47.5 - 14
X > 33.5
so X >= 34 or X at least 34
proof : sub. 34 into X, [(X + 14) - 19] / (X + 14) = 29/48 = 0.604 (> 3/5);
but if sub. 33 into X, [(X + 14) - 19] / (X + 14) = 28/47 = 0.596 (< 3/5) !
since remained students more than 3/5 of original (X + 14), so 19 of them must less than 2/5 of original.
(X + 14) > 19 x 5/2
X > 47.5 - 14
X > 33.5
so X >= 34 or X at least 34
proof : sub. 34 into X, [(X + 14) - 19] / (X + 14) = 29/48 = 0.604 (> 3/5);
but if sub. 33 into X, [(X + 14) - 19] / (X + 14) = 28/47 = 0.596 (< 3/5) !
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