age problem to be solved by system of 2 equations (Sadie's daughter's age)

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allegansveritatem

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I spend most of an hour today trying to get a plausible solution to this problem to no avail: 7 years ago a daughter was 1/3rd as old as her mom was then. In 7 years the mom will be twice as old as her daughter was then. How old are they now?

I set this up thus:

x=mom's age, y=daughter's age

y-7= 1/3(x-7)
Y+7= 2(1/3(x-7)) which, after clearing fractions, develops to:

-3x+3y-21=-21
-7x+3y=-7 which eventually resolves to:

x=-3.5 ?????

here is a photo of the problem--in two parts:ageproblem1.PNGageproblem2.PNG

What am I missing here?
 
I just reread the problem and I think I may have misread. I am going to rework the problem now and get right back.


no. I still don't come out right. What am I doing?. I think I am going wrong in more ways than one.
 
Last edited:
allegansveritatem said:
I spend most of an hour today trying to get a plausible solution to this problem to no avail: 7 years ago a daughter was 1/3rd as old as her mom was then. In 7 years the mom will be twice as old as her daughter was then. How old are they now?

I set this up thus:

x=mom's age, y=daughter's age

y-7= 1/3(x-7)
Y+7= 2(1/3(x-7)) which, after clearing fractions, develops to:

-3x+3y-21=-21
-7x+3y=-7 which eventually resolves to:

x=-3.5 ?????

here is a photo of the problem--in two parts:View attachment 9415View attachment 9416

What am I missing here?
Click to expand...
In 7 years the mom will be twice as old as her daughter was then. First realize that will be means equal, In 7 years the mom means x+7 and twice as old as her daughter was then means 2 times the age of the daughter then. Now as YOU wrote the then refers to the daughter 7 years ago which you denoted correctly as y-7. So twice as old as her daughter was then means 2(y-7). Please continue from here
 
allegansveritatem said:
I spend most of an hour today trying to get a plausible solution to this problem to no avail: 7 years ago a daughter was 1/3rd as old as her mom was then. In 7 years the mom will be twice as old as her daughter was then. How old are they now?

I set this up thus:

x=mom's age, y=daughter's age

y-7= 1/3(x-7)
Y+7= 2(1/3(x-7)) which, after clearing fractions, develops to:

-3x+3y-21=-21
-7x+3y=-7 which eventually resolves to:

x=-3.5 ?????

here is a photo of the problem--in two parts:View attachment 9415View attachment 9416

What am I missing here?
Click to expand...

I see two mistakes. One is in copying the problem; the original says "as she will be then" (in the future), not "as her daughter was then" (in the past). The second is in swapping the meanings of x and y when you wrote your second equation.
 
Dr.Peterson said:
I see two mistakes. One is in copying the problem; the original says "as she will be then" (in the future), not "as her daughter was then" (in the past). The second is in swapping the meanings of x and y when you wrote your second equation.
Click to expand...

Thanks for the tips. I will go back at this tomorrow and report back.
 
Jomo said:
In 7 years the mom will be twice as old as her daughter was then. First realize that will be means equal, In 7 years the mom means x+7 and twice as old as her daughter was then means 2 times the age of the daughter then. Now as YOU wrote the then refers to the daughter 7 years ago which you denoted correctly as y-7. So twice as old as her daughter was then means 2(y-7). Please continue from here
Click to expand...

I'm afraid I read the problem wrong...it says: in 7 years the mom will be twice the age that her daughter WILL have then. So...I will have to come back to this problem in the morning. It is 1 am and my poor brain is fried.
 
allegansveritatem said:
I have tried this and I get this: x-3y=0
x-2y=0

An impossible situation. No?
Click to expand...
Yes, these two equations results in both x and y being 0.
[1]: x - 7 = 3(y - 7)

[2]: x + 7 = 2(y + 7)

Try again, and this time distribute the 2 and 3 to the 7 as well as the y.
 
Jomo said:
Yes, these two equations results in both x and y being 0.
[1]: x - 7 = 3(y - 7)

[2]: x + 7 = 2(y + 7)

Try again, and this time distribute the 2 and 3 to the 7 as well as the y.
Click to expand...

Yes, this will work. I came upon this before I read your post today so I know this is right from the ground up, so to speak. I was making all kinds of goofy little mistakes-as usual. I will present my results in next post. Thanks for your earlier help. I know now where I was going wrong.
 
I worked on this again today and after a few more false starts I think I found where I was going wrong--almost everywhere!
Here is how I finally solved it.


X=mom's present age
y=daughter's present age


1/3x -7=y-7
2y+7=x+7


3y-21=x-7
2y+7=x+7


-x+3y=14
-x+2y=-7


-x+3y=14
-1(-x+2y=-7) or x-2y=7


y=21


So when daughter seven years ago was 14 she was 1/3 mom's age then which had to be 42. Now, therefore, 7 years later, mom is 49. And 7 years hence, when daughter will be, then, at 28, half the age of mom, mom will be 56.


So: X=49 Y=21


Does this look right? Thanks to all for the help. I got some good tips.
 
allegansveritatem said:
I worked on this again today and after a few more false starts I think I found where I was going wrong--almost everywhere!
Here is how I finally solved it.

X=mom's present age
y=daughter's present age

1/3x -7=y-7
2y+7=x+7

3y-21=x-7
2y+7=x+7

-x+3y=14
-x+2y=-7

-x+3y=14
-1(-x+2y=-7) or x-2y=7

y=21

So when daughter seven years ago was 14 she was 1/3 mom's age then which had to be 42. Now, therefore, 7 years later, mom is 49. And 7 years hence, when daughter will be, then, at 28, half the age of mom, mom will be 56.

So: X=49 Y=21

Does this look right? Thanks to all for the help. I got some good tips.
Click to expand...

Everything is correct, except for the equations you wrote! You are still omitting parentheses that are essential.

Rather than

1/3x -7=y-7
2y+7=x+7

you should have (and apparently knew that you meant)

1/3(x - 7) = y - 7
2(y + 7) = x + 7

 The solution to the equations you wrote is x = 0, y = 0.

On the other hand, the way you wrote the definitions of the variables is perfect, and the fact that you checked the answer by putting it into the original problem, not just the equations, is exactly what I recommend. Good work.
 
Dr.Peterson said:
Everything is correct, except for the equations you wrote! You are still omitting parentheses that are essential.

Rather than

1/3x -7=y-7
2y+7=x+7

you should have (and apparently knew that you meant)

1/3(x - 7) = y - 7
2(y + 7) = x + 7

 The solution to the equations you wrote is x = 0, y = 0.

On the other hand, the way you wrote the definitions of the variables is perfect, and the fact that you checked the answer by putting it into the original problem, not just the equations, is exactly what I recommend. Good work.
Click to expand...

yes, I see that. I distributed as though the brackets were there. I will be more careful with this because it is where I often go astray. I'm knot sure why I omitted them in the post.Thanks for checking it all out.
 
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