→ flac:感激啦 很清楚 大家都挺利害的 08/29 14:57
推 Vert1300533:老實說 這個推論想法比較好 08/29 23:20
※ 引述《flac (老獅子)》之銘言：
: 請教一題GWD數學
: If x, y, and k are positive numbers such that [x/(x+y)](10) + [y/(x+y)](20) = k
: and if x < y, which of the following could be the value of k?
: A. 10
: B. 12
: C. 15
: D. 18
: E. 30
: 答案為D
: 謝謝
原式 = 10X 20Y 10X+20Y 10X+10Y 10Y 10Y
----- + ----- = --------- = -------- + ----- = 10 + ----- = K
X+Y X+Y X+Y X+Y X+Y X+Y
We get 10Y
----- = K-10
X+Y
(A) if K = 10 , then Y = 0 , which contradicts with the premise
" y is positive "
(B) if K = 12 , then 10Y
----- = 2 , and we get X = 4Y , which contradicts
X+Y
with the premise " X<Y "
(C) if K = 15 , then 10Y
----- = 5 , and we get X = Y , which contradicts
X+Y
with the premise " X<Y "
(D) if K = 18 , then 10Y
----- = 8 , and we get Y = 4X , it could be the answer
X+Y
(E) if K = 30 , then 10Y
----- = 20 , and we get Y = -2X , which contradicts
X+Y
with the premise " X and Y are both positive "
Then obviously, (D) is the best answer. #
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