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二元一次聯立方程式應用題疑問

Nov 3rd 2013, 08:31

假設甲.乙兩班各有x.y人

則根據題意:芒果總數/甲班人數=10 ; 芒果總數/乙班人數=15

→芒果總數=10×甲班人數=15×乙班人數

→芒果總數=10x=15y→y=2/3x

同時分給甲.乙兩班:芒果總數/(甲班人數+乙班人數)=每人分得的數量

→每人分得的數量=10x/(x+y)

→每人分得的數量=10x/(x+2/3x)

→每人分得的數量=10x/(5/3x)

→每人分得的數量=10/(5/3)=10×3/5

→每人分得的數量=6顆

假設每公斤的米.糖價格分別為x.y

則根據題意:30x+21y=2×1000-(500+6×10)

→30x+21y=1440 同乘以2/3

→20x+14y=960

即20公斤米和14公斤糖的總價為960元

所以付1000元,應找回1000-960=40元

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