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If x, y, and k are positive numbers such that ( x)(10)/(x + y) + ( y)(20)/(x + y) = k and if x < y, which of the following could be the value of k? 下面的是答案 10x / (x + y) + 20y / (x + y) = k => 10x + 20y = k(x + y) => 20y - ky = kx - 10x => (20 - k)y = (k-10)x, since we knot the fact that x < y, then (k - 10) must be greater than (20 - k) in order for (20 - k)y to be equal to (k -10)x; so out of all the choices we were given, we want one that makes (k - 10) > (20 - k): A.
10 => 20 - k = 10, k - 10 = 0 => not this one B.
12 => 20 - k = 8, k - 10 = 2 => not this one C.
15 => 20 - k = 5, k - 10 = 5 => not this one D.
18 => 20 - k = 2, k - 10 = 8 => bingo!!! E.
30 => 20 - k = -10, k - 10 = 20, even though this one does make k - 10 > 20 - k, but k - 10 turns out to be negative, since x and y are positive integers and (k - 20)x > 0 thus this can't be the answer 我想问的是 10x + 20y = k(x + y) => 20y - ky = kx - 10x 可以推出 (20 - k)y = (k-10)x, 但是也可以推出 （10-k）> (k-20) 如果是后者，天，是算出来k<15的！！！ 这道题怎么回事？？？ | 
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发表于 2006-7-25 11:36:00
