Question 816678
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.