# Linear Equation.

1. Jan 15, 2013

### blunted

1. The problem statement, all variables and given/known data

The age of a mother is twice the sum of ages of her 2 sons. 5 years later the mother will be 20 years older than the sum of ages of her sons. What age is the mother today?

2. Relevant equations

3. The attempt at a solution

M - mother ; S1 = son1 ; S2 = son2. S = S1 + S2.

http://sketchtoy.com/18509468

Thanks.

2. Jan 15, 2013

### Staff: Mentor

You can check your solution on your own. Do the values you found for the ages of the mother and the two sons satisfy the conditions given in the problem?

3. Jan 15, 2013

### blunted

I did all that, of course. But I still have an inkling that I'm doing something wrong.

4. Jan 15, 2013

### Staff: Mentor

What do you get for the mother's age now?
What do you get for the sum of the ages of the two sons now?
Please write these here, not on some sketchpad web site.

5. Jan 15, 2013

### blunted

Mother's age: 30.
The sum of her sons ages: 15

6. Jan 15, 2013

### Staff: Mentor

OK, so right now, the mother's age is two times the sum of the sons' ages. That checks.

In 5 years, the mother will be 35, and the sum of the sons' ages will be 25. That doesn't check.

You might have forgotten that in 5 years, each son will be 5 years older, so the sum of their ages will have increased by 10.

7. Jan 15, 2013

### blunted

But I found the mother's age today. 5 years after.

8. Jan 15, 2013

### Dick

Still wrong. What linear equations are you solving? Ok, I looked at the sketchtoy thing. You've got M=2S now. The sons age too. In 5 years the equation will become M+5=(S+10)+20.

Last edited: Jan 15, 2013
9. Jan 15, 2013

### blunted

I cannot wrap my head around it. No matter how much I tried.

10. Jan 15, 2013

### Dick

Why? Now M=2S. You wrote that and I agree. In five years M changes to M+5 because the mother ages 5 years and S changes to S+10 because each son ages 5 years. Then you have M+5=(S+10)+20 since the mother's age is then 20 years older than the sum of the sons ages. What's so mind blowing?

11. Jan 15, 2013

### blunted

Seems like too much maths is not good. I head off to bed. Thanks for the help.

12. Jan 15, 2013

### Dick

Sure, think it over after some rest. It'll probably seem much easier.

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