SOLUTION: Hello, We are trying to follow this equation and solution. Any help to show the work would be great thanks Juan is 2 years older than Sylvia. Four years ago, Sylvia was 5/6t

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Question 1061082: Hello, We are trying to follow this equation and solution. Any help to show the work would be great thanks
Juan is 2 years older than Sylvia. Four years ago, Sylvia was 5/6th of Juan's age. How old are both now?
Found 2 solutions by addingup, MathTherapy:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
J = S+2 or we can state it as S = J-2. Next we'll use J-2 for S.
S-4 = 5/6(J-4) remember, 4 year ago they were BOTH 4 yrs younger
``````````````
Substitute for S and distribute 5/6 on right (distributive property of multiplication 2(2+3) is the same as 4+6)
````````````
J-2-4 = 5/6J-20/6 add/subtract on left and simplify the fraction, divide up/down by 2:
J-6 = 5/6J-10/3 now it's just algebra from here on:
`````````
J-6+10/3 = 5/6J add on left. Any number can be turned into a fraction, every number is divisible by itself and by 1: -6/1+10/3 multiply -6/1 times 3/3 to get a common denominator: -18/3+10/3 = -8/3`
```````````
Now we have:`
J-8/3 = 5/6J
J = 5/6J+8/3
J-5/6J = 8/3
OK, now subtract 5/6 J from J. J is just 1 J and like we said, we can turn it into a fraction like this: 1/1
So: 1/1-5/6 = 6/6-5/6 = 1/6
`````````
And now we have:`
1/6J = 8/3 divide both sides by 1/6
J = 8/3*6/1 = 48/3 = 16/1 or just 16
Juan is 16. And Sylvia is 16-2 = 14
----------------------------
Check, 4 years ago
J = 16-4 = 12
S = 14-4 = 10
Sylvia was 5/6 of J's age (5/6 of 12)
12*5/6 = 60/6 = 10 Sylvia was 10 - Correct
-----------------
Lots of typing, here's hoping it helps.
John



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Hello, We are trying to follow this equation and solution. Any help to show the work would be great thanks
Juan is 2 years older than Sylvia. Four years ago, Sylvia was 5/6th of Juan's age. How old are both now? 
Let Sylvia's age be S

Then Juan's is: S + 2

Four years ago, Sylvia was S - 4

Four years ago, Juan was: S + 2 - 4, or S - 2

Since 4 years ago, Sylvia was  Juan's age, THEN, we get:  

6S - 24 = 5(S - 2) ------- Multiplying by LCD, 6

6S - 24 = 5S - 10

6S - 5S = - 10 + 24 

S, or Sylvia is: 

Jaun is: 14 + 2, or 

That's it....nothing COMPLEX! 

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