SOLUTION: Marianne is 4 years older than Anna and 2 years older than Khate. 4 years ago, thrice Marianne's age devided by Anna's age was # years less than Khate's age. Find their present age

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Question 938059: Marianne is 4 years older than Anna and 2 years older than Khate. 4 years ago, thrice Marianne's age devided by Anna's age was # years less than Khate's age. Find their present ages?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
m = Maria's present age
a = Ann's present age
k = Kate's present age
:
Write an equation for each statement
:
Marianne is 4 years older than Anna and 2 years older than Khate.
m = a + 4
or
a = (m-4)
:
m = k + 2
or
k = (m-2)
;
4 years ago, thrice Marianne's age divided by Anna's age was 3 years less than Khate's age.
%283%28m-4%29%29%2F%28a-4%29 = (k-4) - 3
%28%283m-12%29%29%2F%28a-4%29 = k - 7
replace a with (m-4) and k with (m-2)
%28%283m-12%29%29%2F%28%28m-4%29-4%29 = (m-2) - 7
%28%283m-12%29%29%2F%28%28m-8%29%29 = m - 9
3m - 12 = (m-8)(m-9)
3m - 12 = m^2 - 17m + 72
Combine like terms on the right
0 = m^2 - 17m - 3m + 72 + 12
A quadratic equation
m^2 - 20m + 84 = 0
Factors to
(m-6)(m-14) = 0
Two solutions
m = 6, not a reasonable answer
m = 14 yrs is Maria's age
then
a = 14 - 4 = 10 yrs is Ann's age
and
k = 14 - 2 = 12 yrs is Kate's age