Twice the age

Algebra Level pending

"I'm twice the age you were when I was the age you are and when you will be the age that I am the sum of our ages will be 54."

What are the ages of the two guys in the conversation? Write the two ages consecutively without space. For example, if the speaker is 10 years old and the other 20, write 1020.


The answer is 2418.

Mirko Busonero by Mirko Busonero , 31, Italy

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Mirko Busonero
Aug 21, 2016

Let x x and y y the two ages we have to found. If z is the difference between x and y we have

  • "the age you were when I was the age you are"=y-z

  • "the sum of our age when you will be the age that I am"=x+z+y+z=x+y+2z

So we have an equation system:

x=2(y-z)
x+y+2z=54

Replacing z=x-y we have:

x=2(y-(x-y))
x+y+2(x-y)=54

Solving this we get the solution:

x=2(y-x+y)
x+y+2x-2y=54
x=2(2y-x)
3x-y=54
x=4y-2x
3x-y=54
3x=4y
3x-y=54
3x=4y
3y=54
x=24
y=18
1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...