Question 170277: Five girls live in the same apartment building. To determine the age of each girl, write each clue as an equation or an inquality.
1. All 5 girls are older than 10 but younger than 20.
2. Karen i solder than Angela but younger than Janet.
3. Janet's age is halfway between Tamara's age and Angela's age.
4. The ages of all the girls except Janet are even numbers.
5. Susan is neither the oldest nor the youngest.
6. Karen is as much older than Angela as Tamara is older than Susan.
7. No two girls are the same age.
Found 2 solutions by Mathtut, checkley77:
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! lets call a,k,j,s,t the ages of the girls angela,karen,janet,susan,and tamara respectively.
1.  so there ages are between 11 and 19
2.  but 
3. 
4. all ages except j is divisible by 2
5. susan neither youngest or oldest
6. k-a=t-s
7. a is not equal to k is not equal to j is not equal to s is not equal to t
:
:
because of #4 everyone but Janet has to be 12,14,16 or 18
because of #'s 2,6,and 5 there are only 2 possibilities
:
k-a must equal t-s meaning 2=2 or 4=4
:
A. angela-12,karen-14,susan-16,tamara-18----->14-12=18-16 or 2=2
:
B. angela-12,susan-14,karen-16,tamara-18----->16-12=18-14 or 4=4
:
lets determine # 3. at this point in either case A or B j=(18+12)/2=15 so Janet is 15 which fits right into # 4. which states Janets age is not even.
:
now we know that choice B will not work because of 2. which states that karen is less than janet......leaving only choice A.
conclusion 
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! 1. All 5 girls are older than 10 but younger than 20.
2. Karen i solder than Angela but younger than Janet.
3. Janet's age is halfway between Tamara's age and Angela's age.
4. The ages of all the girls except Janet are even numbers.
5. Susan is neither the oldest nor the youngest.
6. Karen is as much older than Angela as Tamara is older than Susan.
7. No two girls are the same age.
10>A,K,J,S,T<20
A MUST BE 12 OR GREATER.
T MUST BE 18 OR LESS.
(T-K)/2=J [J MUST BE ODD, T&K ARE EVEN THUS (T-K=6), 18-12=6]
A+X=K X [MUST BE 2 & BOTH ARE EVEN NUMBERS]
S+X=T [DITTO]
Angela=12 \
Karen=14 \
Janet=15 > ANS.
Susan=16 /
Tamara=18 /
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