Question 80948: I need to know how old your three kids are. The product of their ages is 36.
The sum of their ages is the same as my house number. The younger two are twins.
How old are the kid's and what is my house number.
I think that the kids are 2 and 9 and the house number is 13 but I cannot figure out an equation. This didn't come from a textbook. It is an extra credit paper.
Found 2 solutions by scott8148, Edwin McCravy:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! let a=youngest, b=next, c=oldest, and h=house
a*b*c=36 ... a+b+c=h ... a=b ... a < c ... 
factors of 36 are 1 & 36, 2 & 18, 3 & 12, 4 & 9, 6 & 6 ... this leaves 1, 4, and 9 as possibilities for 
1,1 & 36 is least likely ... 2,2 & 9 and 3,3 & 4 seem equally likely as possible age scenarios
as you can see, more information is needed to arrive at a unique solution
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! : I need to know how old your three kids are. The product of their ages is 36.
The sum of their ages is the same as my house number. The younger two are twins.
How old are the kid's and what is my house number.
I think that the kids are 2 and 9 and the house number is 13 but I cannot figure out an equation. This didn't come from a textbook. It is an extra credit paper.
I suspect there is more than one solution.
Let the twins' age be t and the older child's age be c.
>>...The product of their ages is 36...<<
Translation into an equation: t x t x t = 36, or
t²c = 36
Solve for t.
Divide both sides by c
t² = 36/c
Take positive square roots of both sides
_
t = 6/Öc
The twins are younger than the older child, so
t < c
_
so substitute 6/Öc for t in that inequality
_
6/Öc < c
Square both sides
36/c < c²
Multiply both sides by c, which is positive
so the symbol of inequality will stay the same:
36 < c³
Take cube roots of both sides:
3.301927249 < c
_
Since t = 6/Öc,
_
vc must divide evenly ito 6
The only divisiors of 6 are 1, 2, 3, and 6, so
_
Öc must be 1, 2, 3 or 6, so
c must be 1, 4, 9, or 36
But c must be greater than 3.301927249 so
c is either 4, 9, or 36, so
_ _ __
t must be 6/Ö4, 6/Ö9 or 6/Ö36, that is
t must be 6/2, 6/3, or 6/6, that is,
t must be 3, 2, or 1
The three possibilities are
1. the twins are 3 and the older child is 4,
and the house number is 3 + 3 + 4 = 10
2. the twins are 2 and the older child is 9,
and the house number is 2 + 2 + 9 = 13,
(which was your solution)
3. the twins are 1 and the older child is 36.
and the house number is 1 + 1 + 36 = 38
You might rule out case 3, since 36 is a little old
for a kid. Also the mother of a 36-year-old would be
too old to have 1-year-old twins, for she'd be past
menopause! Hahaha. But the first two are both possible
solutions.
Edwin
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