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？

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.

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.