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ｌａｓｔｍａｔｈｓ題唔該
發問:
一個盒入面共有300枚金幣.其中的N枚是50c/金幣,而其餘的是$2金幣.該批金幣總值是$300,問共有多少枚$2金幣?
最佳解答:
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50cents的金幣=N枚 $2金幣=(300 - N)枚 $0.5N + $2(300 - N) = $300 0.5N + 600 - 2N = 300 600 - 1.5N = 300 1.5N = 300 N = 200 $2金幣=300 - (200) $2金幣=100枚 所以答案係 100枚。
其他解答:
Let a be the no of 50 c (i.e.$0.5) and b be the no of $2 coins : 0.5a+2b=300.......................(1) a+b=300..............................(2) (1) x 2 : 2(0.5a+2b)=300x2 a+4b=600................(3) (3)–(2) : (a+4b)-(a+b) = 600-300 a+4b-a-b = 300 3b = 300 b=100 ∴There are 100 $2 coins|||||設五毫(50c)為x, $2為y 得出兩條方程式..... 300 = x + y---------(1) 300 = 0.5x + 2y---------(2) 由(1) y = 300 - x--------(3) 代(3)入(2) 300 = 0.5x + 2(300 - x) x = 200 所以y = 100 $2金幣有100個|||||0.5N + 2 ( 300 - N ) = 300 0.5N + 600 - 2N = 300 -1.5N = -300 N = 200 Checking : 0.5( 200 ) + 2 ( 300 - 200 ) = 300 100 + 200 = 300 300 = 300 200枚是50c/金幣 , ( 300 - N ) = 100枚是 $2金幣.|||||(0.5 x N ) + ( 2 x (300 - N)) = 300 0.5N + (600 - 2N) = 300 0.5N + 600 - 2N = 300 -1.5N + 600 = 300 -1.5N = 300 - 600 -1.5N = -300 N = 200|||||0.5N+2(300-N)=300 1.5N=300 N=200 所以共有300-200=100枚$2金幣A215E4A2B88AAE64
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