Question 1120446: When Juanita is as old as her mother is now, she will be five times as old as her son is now. By then, Juanita's son will be 8 years older than Juanita is now. Juanitas age combined with her mothers age, equals 100 years. how old is Juanita's son?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Assigning variables and carefully transcribing the description into equations:
PERSON VARIABLE IN x YEARS
Juanita J J+x
Son y y+x
Mother m m+x
The question asks for J.
Steps can be different. First step could be, substitute for m wherever possible,...
May find that J is 35.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The other tutor didn't show a complete solution, so I don't know how much work remained to reach the answer from where they left off. In any case, I get a different answer than they did....
There are many different ways the problem can be set up; the method I used shown below may not be the easiest or most efficient....
Let m be the mother's current age
Then 100-m is Juanita's current age, since the sum of their ages is 100.
Let s be the son's current age.
The number of years until Juanita is her mother's current age is the difference of their current ages: m-(100-m) = 2m-100.
According to the statement of the problem, m is Juanita's age "then".
The son's age "then" is s + (2m-100).
Juanita "then" will be 5 times as old as her son is now:
(1) m = 5s.
Her son's age "then" will be 8 more than Juanita's current age:
(2) s+2m-100 = 108-m --> s+3m = 208.
Substitute (1) in (2) to find s, the son's current age.
s+3(5s) = 208
s+15s = 208
16s = 208
s = 13
The son's current age is 13.
So the mother's current age is 5(13) = 65.
So Juanita's current age is 100-65 = 35.
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