SOLUTION: The sum of the ages of the two students is 36. Four years from now the ratio of their will be 4:7. Find their present ages?

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Question 620790: The sum of the ages of the two students is 36. Four years from now the ratio of their will be 4:7. Find their present ages?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two students, a & b, ages now
:
Write an equation for each statement:
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The sum of the ages of the two students is 36.
a + b = 36
b = (36-a); use this for substitution
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Four years from now the ratio of their will be 4:7.
%28a%2B4%29%2F%28b%2B4%29 = 4%2F7
CRoss multiply
7(a+4) = 4(b+4)
7a + 28 = 4b + 16
7a = 4b + 16 - 28
7a = 4b - 12
Replace b with (36-a)
7a = 4(36-a) - 12
7a = 144 - 4a - 12
7a + 4a = 144 - 12
11a = 132
a = 132/11
a = 12 yrs now
then
b = 36 - 12
b = 24 yrs now
:
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Check this; add 4 yrs to their ages, and see what the ratio is.
16%2F28 = 4%2F7