SOLUTION: 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

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 /

RELATED QUESTIONS
Five girls live in the same apartment building. To determine the age of each girl, write... (answered by ankor@dixie-net.com)
an apartment building has 45 windows on each side. each window is a rectangle that is... (answered by josmiceli)
an apartment building has 7 stories. The top floor is one large apartment. Each floor... (answered by rfer)
1. Samuel is 2/3 as old as his brother. In five years, he will be 3/4 as old as his... (answered by richwmiller)
All the units in an apartment building have either one or two bedrooms. The five story... (answered by richwmiller)
The problem reads as follows: Ideally, a school district would like the boy/girl ratio... (answered by stanbon)
Jenny, Bryan, and Tommy live in the same apartment building with apartment numbers that... (answered by jorel1380)
1) A girl is x years old. Her father is three times as old. If the difference in their... (answered by jorel555)
The favorite colors of Betty, Carol, Nick, and Joe are green, pink, red, and yellow. Use... (answered by xcentaur)