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

In summary, the mother is currently 30 years old and the sum of the ages of her two sons is 15. In 5 years, the mother will be 35 and the sum of the sons' ages will be 25.
  • #1
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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  • #2
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?
 
  • #3
I did all that, of course. But I still have an inkling that I'm doing something wrong.
 
  • #4
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
Mother's age: 30.
The sum of her sons ages: 15
 
  • #6
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.

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
But I found the mother's age today. 5 years after.
 
  • #8
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.
 
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  • #9
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.
 

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

What is a linear equation?

A linear equation is an algebraic equation that contains only variables with a degree of 1 and has a constant term. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

How do you solve a linear equation?

To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by using inverse operations such as addition, subtraction, multiplication, and division to both sides of the equation until the variable is alone on one side.

What is the significance of "Mother's Age w/ 2 Sons" in a linear equation?

The phrase "Mother's Age w/ 2 Sons" can be represented as a linear equation because it involves two variables (the mother's age and the age of her two sons) and can be solved using algebraic methods.

Can you give an example of solving a linear equation for "Mother's Age w/ 2 Sons"?

For example, if the sum of the ages of the mother and her two sons is 50 years and the mother's age is 2 years more than twice the age of her older son, we can write the following linear equation: x + y + z = 50, where x is the mother's age, y is the age of the older son, and z is the age of the younger son. This equation can be solved to find the specific ages of the mother and her two sons.

How are linear equations useful in real life situations?

Linear equations are useful in real life situations because they can help us model and solve real-world problems. They are often used in fields such as economics, engineering, and physics to make predictions and analyze data. In the case of "Mother's Age w/ 2 Sons," it can help us determine the ages of the mother and her two sons based on given information.

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