"How old is Kristen?" using other people's ages for clues.

Question

Kristen is 4 times Claire's age.  Emily is 6 years older than Claire, and 6 years younger than Zack.  If Anna is twice as old as claire, and the total of their ages is 81 - how old is Kristen?

Answer 1

     Kristen + Claire  +            Emily + Zack  + Anna          = 81

 

(4 Claire) + Claire + (Claire + 6) + Zack + (2 Claire) = 81

( Claire + 6 ) = Zack - 6

 

8 Claire + Zack =  81

   Claire  - Zack = -12  -----> Zack = Claire + 12

 

9 Claire = 63

 

Claire = 7 years

 

Kristen = 28 years

 

Anna = 14 years

 

Emily = 13 years

 

Zack = 19 years

 

 

 

 

 

 

Answer 2

The first thing to do is assign a variable.  A lot of the ages are compared to Claire's, so the best thing to do would be to assign a variable to her age.  Call it x.

 

Now follow exactly what the problem says about the other ages and write them in terms of x.

 

Kristen's age is 4x.

 

Emily's age is x + 6.

 

Zack is 6 years older than Emily, so his age is x + 6 + 6 = x + 12.

 

Anna's age is 2x.

 

Add all the ages together:  x + 4x + (x + 6) + (x + 12) + 2x, and that should be equal to 81.

 

x + 4x + (x + 6) + (x + 12) + 2x = 81

 

Gather all the terms together:

9x + 18 = 81

 

Solve:

9x = 63

x = 7

 

Remember that Kristen's age is 4x, so she must be 28.