Age word problem three variables: In 2006 Becky is 2.5 times Anna's age, Mary is 2X

[patelsm]

Hi folks,

Got another one that we are struggling with:

In November 2006 Becky is two and half times Anna's age and Mary is twice Anna's age.
In November 2009 Anna is half of Becky's age. Mary is six years older than Anna.
How old are the three girls in November 2009.

Below is my attempt

November 2006
Becky, B=2.5A where A is Anna's age.
Mary, M = 2A

November 2009
Becky B's age is B+3
Anna's age A+ 3
Mary's age is M+3
A = (B+3)/3
M = 6 + (A+3)

So I use M = 6 + (A+3) as an equation to work out A
replace M by 2A (from November 2006)
2A = 6 + (A + 3)
A = 9

in November 2009 A is 12
M is 18 + 3 = 21
B is 25.5

this does not look right to me. Any help please.

thanks,
saf

 

[HallsofIvy]

Hi folks,

Got another one that we are struggling with:

In November 2006 Becky is two and half times Anna's age and Mary is twice Anna's age.
In November 2009 Anna is half of Becky's age. Mary is six years older than Anna.
How old are the three girls in November 2009.

Below is my attempt

November 2006
Becky, B=2.5A where A is Anna's age.
Mary, M = 2A

November 2009
Becky B's age is B+3
Anna's age A+ 3
Mary's age is M+3
A = (B+3)/3
M = 6 + (A+3)

Good to start with but in 2009 Anna's age is A+ 3 so "Anna is half of Becky's age" is A+ 3= (B+ 3)/2 and "Mary is six years older than Anna" is M+3= 6+ (A+ 3). I assume the '/3' was a typo but, after having said that "in 2009 Anna's age Is A+ 3 and Mary's age is M+ 3", you did not put those into the equations.

So I use M = 6 + (A+3) as an equation to work out A
replace M by 2A (from November 2006)
2A = 6 + (A + 3)
A = 9

in November 2009 A is 12
M is 18 + 3 = 21
B is 25.5

this does not look right to me. Any help please.

thanks,
saf

 

[Denis]

In November 2006 Becky is two and half times Anna's age and Mary is twice Anna's age.
In November 2009 Anna is half of Becky's age. Mary is six years older than Anna.

Reword slightly to make it CLEARER:
Now, Becky is 2.5 times Anna's age and Mary is twice Anna's age.
In 3 years, Becky will be twice Anna's age and Mary will be 6 years older than Anna.

ALWAYS declare your variables:
a = Anna's age now, b = Becky's age now, m = Mary's age now

Now:
Anna = a, Becky = 2.5a, Mary = 2a
In 3 years:
Anna = a+3, Becky = 2(a+3), Mary = a+3+6

Carry on....