Solve Linear Equation: Mother's Age w/ 2 Sons

[blunted]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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

http://sketchtoy.com/18509468

Thanks.

 

[Mark44]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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

http://sketchtoy.com/18509468

Thanks.

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?

 

[blunted]

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

 

[Mark44]

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.

 

[blunted]

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

 

[Mark44]

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

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.

 

[blunted]

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

 

[Dick]

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

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.

 

[blunted]

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

 

[Dick]

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

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?

 

[blunted]

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

 

[Dick]

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

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