Algebra problem...

[Dayle in Guatemala]

Could you all help me out with this?

Ellen is 11 years older than Maja. Last year Ellen was twice as old as Maja. How old is Maja now?

Here's our solution:

Ellen Maja

Last year: 2x x-1
This year: 11+x x

11+x=3(x-1)
11+x=3x-3
14+x=3x
14=2x

Maja is 7 years old.


Their solution:

Ellen Maja

Last year: x+10 x-1
This year: x+11 x


x+10=2(x-1)
x+10=2x-2
10=x-2
12=x

Maja is 12 years old.


First of all, where did they get the x+10? And where did they get the 2(x-1)?
And what happened to the x+11?

I'm confused!

[Jann in TX]

First if you were to check your answer you would find out that it is not correct...

They used x +10 for Ellens age last year (they skipped a step) because Ellen was 11 years older than Maja BUT Maja was one year younger than she is now...so that would make Ellen = x-1 +11 or Maja's age last year plus 11 x+10.

2(x-1) is also correct. Last year Ellen was twice Maja's age LAST YEAR.

HTH

[Kate in Arabia]

This year Ellen is 11 years older:

Ellen = x+11

Last year Ellen was twice as old, but Maja was a year younger:

2(Maja's age-1 year)
Ellen = 2(x-1)

BUT, Ellen was also a year younger last year:
Ellen -1 year = 2(x-1)

Which is why, when the two equations are put together, it becomes:

x+11 (-1) = 2(x-1)

x+10 = 2(x-1)


Did that make sense?

[Dayle in Guatemala]

Got it!!!! Thanks so much. This is why we use a cd-rom for regular algebra. I'm not a math person!

[LilyK]

instead of subtracting a year, I added a year at the end. I thought that was easier to understand.

E=M+11
Last year,
E=2M
therefore,
M+11=2M
M=11
This was last year, so this year
M=11+1
M=12

Is that a little simpler?