SOLUTION: Marie is 10 years older and her sister, Sarah, is 8 years old. How many years ago was Marie twice as old as Sarah was then? We know that Marie is now 18 years old but is it aski

Question 1100456: Marie is 10 years older and her sister, Sarah, is 8 years old. How many years ago was Marie twice as old as Sarah was then?
We know that Marie is now 18 years old but is it asking how many years ago Marie was twice as old as Sarah was at age 8? Or just twice her age? Not sure how we would put this into an equation. This is for third grade math!
Found 4 solutions by josmiceli, jorel1380, greenestamps, josgarithmetic:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
is Marie's age now
is Sarah's age now
----------------------------------------
They want to look back into the past and
compare their ages back then. Note that
the difference in their ages will always be
years.
----------------------------------------
Let = the number of years ago that
Marie was twice as old as Sarah was then
----------------------------------------

Add to both sides

----------------------------
I conclude that there was no time in the past when
Marie was twice Sarah's age, but in 2 years
this will be true
Marie's age:

Sarah's age:

So, in 2 years, Marie will be 20 and Sarah will be 10
---------------------------
I t looks like a mistake in the question since they
want to look at a time in the past when Marie
is twice Sarah's age.
------------------------
Get a 2nd opinion if needed on this

Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
We know Sarah is 8, and Marie is 18. Let n be the number of years ago since Marie was twice Sarahs' age. Then:
18-n=2(8-n)
18-n=16-2n
-n=2
n=-2
-(-2)=+2
Marie will not be twice as old as Sarah for another 2 years
☺☺☺☺
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

You say this is for third grade math. So a solution using algebra doesn't seem appropriate.

So use logical reasoning.

But you also say you aren't sure what the question is asking. That is no surprise, since the problem as you show it is poorly worded. That is especially bad if it is for third graders.

The problem says "Marie is 10 years older and her sister, Sarah, is 8 years old."

Grammatically, that sentence is incomplete. Marie is 10 years older? Older than whom? The only possible interpretation is that she is 10 years older than her sister Sarah -- but the problem should say so: "Marie is 10 years older than her sister Sarah, who is 8 years old."

So now we have the poor presentation of the problem taken care of: Marie is 18 and her sister is 8.
Now let's look at what the problem asks us to find.

"How many years ago was Marie twice as old as Sarah was then?"

To me, the "then" is not only unnecessary, but confusing.

But analyzing the problem logically from here, we have a problem. If Marie is now 10 years older than Sarah, then she will always (for the sake of age problems like this!) be 10 years older.

So the time when Marie will be twice as old as her sister is when Marie is 20 and Sarah is 10.

But that is two years from now -- not some number of years ago.

So my assessment is that this is an extremely poorly written problem for any age, but especially for young students who are trying to learn from working the problem. The grammar used in the statement of the problem is poor; and the question that is asked has no answer.
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Third grade math???

Marie and Sarah (her sister?)

Sarah is 8 and if Marie is 10 years older, then Marie NOW is 18.

----------------------------------------------------------------
How many years ago was Marie twice as old as Sarah was then?
----------------------------------------------------------------

x years ago.

-----------meaning, not two years ago, but two years FROM NOW, IN THE FUTURE.
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