SOLUTION: Please Help.. Five years ago, Roel was three times as old as his brother, Tony. In 10 years, he will be 10 years older than Tony. Find their present ages.

Question 816678: Please Help..
Five years ago, Roel was three times as old as his brother, Tony. In 10 years, he will be 10 years older than Tony. Find their present ages.
Found 2 solutions by Theo, LinnW:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal roel's age now.
let y = tony's age now.
five years ago, roel was x-5 years old.
five years ago, tony was y-5 years old.
five years ago, roel was 3 times as old as tony.
this means that:
(x-5) = 3 * (y-5)
simplify this to get:
x-5 = 3y - 15
add 5 to both sides of this equation to get:
x = 3y - 10
you now have the value of x in terms of y.
you're still not there yet.
you are also told that in 10 years raul will be 10 years older than tony.
if raul is x years old now, then raul will be x + 10 years old in 10 years.
if tony is y years old now, then tony will be y + 10 years old in 10 years.
in 10 years, raul will be 10 years older than tony.
this means that:
x + 10 = (y + 10) + 10 which can be simplified to:
x + 10 = y + 20
you can solve for x again to get:
x = y + 10
you now have 2 equations for x.
the first equation is:
x = 3y - 10
the second equaton is:
x = y + 10
since 2y-10 and y+10 are both equal to x, you can set them equal to each other and solve for y.
you get:
3y-10 = y+10
subtract y from both equations and add 10 to both sides of this equation to get:
2y = 20
divide both sides of this equation by 2 to get:
y = 10
now that you know that y is equal to 10, you can solve for x in either equation of:
x = y + 10 or x = 3y - 10
if you use x = y + 10, you get x = 10 + 10 = 20
if you use x = 3y - 10, you get x = 30 - 10 = 20
either equation will get you that x = 20.
your solution is:
x = 20
y = 10
5 years ago, x = 15 and y = 5 which means that x equals to 3*y.
10 years from now, x = 30 and y = 20 which means that x equals y + 10.
the equations are both satisfied and the solution is good.

there are several ways to solve this.
i used substitution.
you can also solve by elimination.
you can also solve by graphing.

the whole idea is that you wind up with 2 equations that need to be solved simultaneously to arrive at a solution.

Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Five years ago, Roel was three times as old as his brother, Tony. In 10 years, he will be 10 years older than Tony. Find their present ages.
Set r = age of Roel
Set t = age of Tony
( r - 5 ) = 3(t-5)
( r + 10 ) = ( t + 10 ) + 10
Simplifying
r - 5 = 3t - 15
r + 10 = t + 20
Subtract the bottom equation from the top
-15 = 2t - 35
Add 35 to each side.
20 = 2t
10 = t
Substitute 10 for t in the equation r + 10 = t + 20
r + 10 = 10 + 20
Subtract 10 from each side
r = 20
To check our answer, substitute 10 for t and 20 for r in the equations
( r - 5 ) = 3(t-5)
( r + 10 ) = ( t + 10 ) + 10
( 20 - 5 ) = 3(10-5) so 15 = 3(5) or 15 = 15
( 20 + 10 ) = ( 10 + 10 ) + 10 so 30 = 30
We can say that Roel is 20 and Tony is 10.
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