Question 201494: Would you please help me identify the equation for the following problem:
"Together we are 98 years old. I am twice as old as you were when I was as old as you are now."
I understand A+B=98, but cannot figure the second statement.
Thank you,
Caroline
Found 4 solutions by vleith, ptaylor, valgaze, MathTherapy:
Answer by vleith(2983)   (Show Source):
Answer by ptaylor(2198)  (Show Source):
You can put this solution on YOUR website! "OK Caroline, I started working on this problem early this AM and had to leave. Now I'm back again to finish"
Let x=my age
Then 98-x=your age
Some "y" years ago, you were my age, so:
(98-x)-y=x solve for y
-y=x+x-98 or
y=98-2x That's how many years ago that you were my age. Now we have to subtract this from my current age to find out how old I was then:
My age then=x-(98-2x)=x-98+2x=3x-98
And we are told that you are currently twice that age, so:
(98-x)=2(3x-98) or
98-x=6x-196 subtract 6x and also 98 from each side
-7x=-196-98 or
7x=294 divide each side by 7
x=42--------------------------my age
98-x=98-42=56-----------------your age
CK
14 years ago you were my age (42)
14 years ago I was 28
Sure 'nuff 56 is twice 28
Hope this helps----ptaylor
Answer by valgaze(1) (Show Source):
You can put this solution on YOUR website! Let's pretend that we can only have whole numbers as a solution for their ages, no decimals or fractions.
First things first, let's take inventory of what we know:
1) There are two people whose ages we don't know (let's call them x & y)
2) Their combined ages are 98 years old (x + y = 98)
3) Tricky part: X's age TODAY is twice what Y's age was at the time X was Y's age TODAY. (In other words, in the past X was a certain age, let's say X*, and Y was a certain age, let's say Y*. In algebra terms, being very careful to note we are saying Y* and Y, we could say X=2Y*)
In straight algebra terms, we have the following problem:
1) X+Y=98
2) X=2Y*
We need to figure out a way to solve those equations, if we can even get just one age (X or Y) we will be able figure out the other one, but we have a problem: right now we have more variables than equations (two equations and three unknown variables.)
We either need to come up with another equation/relationship or come up with a clever way to have one of the variables drop/cancel out and solve from there.
The key to this problem is to think about what makes the age between two people special.
For example, imagine you had an older brother or sister, would you ever "catch up" to their age in the future? Unfortunately, and I speak from experience, the "distance" in age between you and your older siblings is a race you will never win. If I am 3 years younger than my sibling today, fifteen years ago I was 3 still 3 years younger and in the future I will still be 3 years younger.
So in our problem, we know another important relationship: The distance between the ages is some constant number D. This distance D applies no matter what time period you are talking about because the distance in age never changes.
So now know:
X-Y=D and X*-Y*=D which crucially means X-Y=D=X*-Y* or finally X-Y=X*-Y*
We have three relationships to play with:
1) X + Y = 98
2) X=2Y*
3) X-Y=X*-Y*
The last thing to think about is what is the relationship between X* and Y. Maybe try drawing a number line labeled 0 to 100 years with X, Y, X*, Y* on it and label the distances between X & Y as D and X* & Y* as D as well and see what you come up with.
Best,
Vic
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Would you please help me identify the equation for the following problem:
"Together we are 98 years old. I am twice as old as you were when I was as old as you are now."
I understand A+B=98, but cannot figure the second statement.
Thank you,
Caroline
Let my age be M, and yours, Y
Then the 1st equation is: M + Y = 98
The 2nd equation which you asked for is: 
When solved, M, or my age, is 56 and yours, or Y, is 42
You should realize from the problem that I am older than you are.
You can do the check!!
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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