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

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Homework Help Overview

The problem involves determining the current age of a mother based on the relationship between her age and the ages of her two sons. It states that the mother's age is twice the sum of her sons' ages, and in five years, she will be twenty years older than the sum of their ages at that time.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationships between the ages, with some expressing uncertainty about their calculations and whether they are interpreting the problem correctly. There are attempts to clarify the equations being used and the implications of aging over time.

Discussion Status

Some participants have provided their current values for the mother's age and the sum of the sons' ages, while others question the validity of these values based on the conditions of the problem. There is ongoing exploration of the equations and relationships involved, with no clear consensus reached yet.

Contextual Notes

Participants are working under the constraints of the problem's conditions and are attempting to reconcile their findings with the requirements laid out in the statement. There is mention of potential misunderstandings regarding the aging process of the sons and the implications for the equations being solved.

blunted
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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.
 
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blunted said:

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?
 
I did all that, of course. But I still have an inkling that I'm doing something wrong.
 
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.
 
Mother's age: 30.
The sum of her sons ages: 15
 
blunted said:
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.[/color]

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.
 
But I found the mother's age today. 5 years after.
 
blunted said:
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.
 
Last edited:
I cannot wrap my head around it. No matter how much I tried.
 
  • #10
blunted said:
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?
 
  • #11
Seems like too much maths is not good. I head off to bed. Thanks for the help.
 
  • #12
blunted said:
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.
 

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