標題:
一家四口，他們年齡的和是76歲，爸爸比媽媽大4歲，女兒比兒子大4歲，5年前全家的年齡的和是58歲。問現在他們各人多少歲？
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一家四口，他們年齡的和是76歲 設 a = 爸爸, b = 媽媽, c = 女兒, d = 兒子 則, 已知: 1) a + b + c + d = 76 2) a - b = 4 3) c - d = 4 4) (a - 5) + (b - 5) + (c - 5) + (d - 5) = 58 => a + b + c + d = 78 從1), 2) 及 3) a + (a - 4) + c + (c - 4) = 76 2a + 2c = 84 a + c = 42 從1) 及 4), 1) a + b + c + d = 76 4) a + b + c + d = 78 兩式沒有解, 兩式相減 = 2, 由此推斷年齡最小的5年前並未出生, 所以 d = 5 - 2 = 3 c = d + 4 = 7 a = 42 - c = 35 b = a - 4 = 31 所以各人今年的歲數是: 爸爸35歲, 媽媽31歲, 女兒7歲, 兒子3歲.
其他解答:
Let x be the age of dad, x-4 be the age of mum Let y be the age of daughter, y-4 be the age of the son x+x-4+y+y-4=76 x-5+x-4-5+y-5+y-5-4=58 2x+2y=84 2x+2y=86 as the age dont match so we know that the son has not born 5years ago the difference is 2 So the son is 5-2= 3 years old the daughter is 3+4=7 years old then 2x+2*7=84 2x+14=84 x=35 So Dad is 35 years old and mum is 31 years old i.e. Son is 3 years old, daughter is 7 years old and Dad is 35 years old while mum is 31 years old now.
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