Thread: Need help with linear equations with one variable

This is the task:

Tim's mother is three times older than Tim. In 14 years, she'll be 2 times older than him. How old are they now?

This text needs to be converted into a linear equoation with one variable and I am supposed to calculate how old is Tim and how old is Tim's mother. I can't seem to get it right. I've tried many different combinations, but I can't.
Please help me, cause I need the answer and I need to know how to solve these types of problems.
Thanks in advance.

Let "t" represent Tim's age, and "m" represent his mother's age.

Since Tim's mother is three times older than Tim, that means m = 3t.

In 14 years, she'll be 2 times older than him. So m + 14 = 2(t + 14).

Can you go from here?

Not quite. I am only allowed to use X as a variable. There is a final result which says that Tim is 14 and his mother is 42. I can't get that result. I tried doing 3X = 2 (x+14), but the result was 28. I tried with (x + 3x) + 14 = 2 (x + 14) + (x + 14) with X representing Tim's age and I got the right result, but I'm not sure if I did it right, or if it was just a coincidence. Did I get it right?

You know that m = 3t and m + 14 = 2(t + 14).

So surely 3t + 14 = 2(t + 14).

Go from here.

3x + 14 = 2 (x + 14)
3x - 2x = 28 - 14
x = 14

Thanks.