Age problem [Solved!]

X

Can u please help me with this problem:
In 10 years' time Ryan will be twice as old as Omar.  !0 years ago he wa 6 times as old.  How old are they both now?  thank you

Relevant page

<a href="/basic-algebra/6-applied-verbal-problems.php">6. Applied Verbal Problems</a>

What I've done so far

I put R = Ryan
O = Omar

then R + 10 = 2O

But I'm stuck there

X

Hello Maria

Good to hear from you again.

This problem is similar to the ones on the page you came from:

<a href="/basic-algebra/6-applied-verbal-problems.php">6. Applied Verbal Problems</a>

You can actually do these by trial and error more quickly (and easier :-), since the number of possible ages is low.

But let's assume you have to do it by algebra.

Let `x` be Ryan's age now and let `y` be Omar's age now.

In 10 years, Ryan's age will be

 `x + 10`

Omar will be

 `y + 10`

From the first sentence,

 `x + 10 = 2(y + 10)`

Do you think you can go on from there?

(BTW, it's maybe not a good idea to use "O" as a variable - it looks too much like 0, the number!)

Regards

X

Hi Murray,

Yes i managed from there

I put from the second sentence

`x-10 = 6(y-10)`

`x-10 = 6y-60`

`x = 6y - 50`

Then 

`x+10 = 2y+20` (from your input)

`x = 2y+10`

SO

`6y - 50 = 2y + 10` (both equal to `x`)

`4y = 60`

`y = 15`.

So Omar is now 15, and this gives Ryan is 40. This works in both statements.

Thank you so much for your help, very much appreciated.

Maria

X

You're welcome, Maria.