SOLUTION: The fairly family are great mathematicians. When asked how old everyone was the family replied, “Our family of two adults and three children is exactly 123 years old altogether”. T

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Question 935064: The fairly family are great mathematicians. When asked how old everyone was the family replied, “Our family of two adults and three children is exactly 123 years old altogether”. The father and son’s ages, when added are 59, which is 5 years less than the mother and the twin girls. The father is three years older than the mother, while the son is three years older than the girls. can you work out each persons age
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
F = father's age
M = mother's age
S = son's age
D = each of the twin daughter's age

>>Our family of two adults and three children is exactly 123 years<< 
F+M+S+2D = 123

>>The father and son’s ages, when added are 59,<<
F+S = 59

which [59] is 5 years less than the mother and the twin girls.
59 = M+2D-5
64 = M+2D

>>The father is three years older than the mother,<<
F = M+3

>>the son is three years older than the girls.<<
S = D+3 

So we have this system of 5 equations in 4 unknowns.
That means we were given more information that we needed.

system%28F%2BM%2BS%2B2D=123%2C+F%2BS=59%2C+64=M%2B2D%2C+F=M%2B3%2C+S=D%2B3%29

Substitute D+3 for S in the first 4 equations and simplify:

system%28F%2BM%2B3D%2B2D=120%2C+F%2BD=56%2C+64=M%2B2D%2C+F=M%2B3%29

Substitute M+3 for F in the first 3 equations and simplify:

system%282M%2B5D=117%2C+M%2BD=53%2C+64=M%2B2D%29

Solve the middle equation for M:  M=53-D. Substitute in the
other 2 equations:

system%282%2853-D%29%2B5D=117%2C+64=53-D%2B2D%29

system%28D=11%2C+11=D%29

So the twin daughters are 11 each.

M=53-D = 53-11 = 42, so the mother is 42.

F=M+3 = 42+3 = 45, so the father is 45.

S=D+3 = 11+3 = 14, so the son is 14.

Edwin

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let Dad's age be represented by , the boy's age be represented by , Mom's age by and each of the twin girls' ages by

Here are some things that we know:











Which is to say:



Substituting 6 into 3 we get

Substituting 4 into 2 we get

The last two equations form a 2X2 system in and . Solve the system by any convenient method to determine the Mom's and the son's ages. The other two ages, Dad and each of the twin girls are simply a matter of arithmetic from that point.

John

My calculator said it, I believe it, that settles it