Question

Five siblings have a combined age of 195 years. The oldest is 13 years older than the youngest, Marc. The middle child, Anne, is five years younger than Josie. The othe two siblings are 6 years apart. If the second oldest child is 42, what are the ages of the siblings?

Answer 1

so five sibbllings ages are repressented as
a,b,c,d,e
let's have a as youngest and e as oldest in that order
total ages are 195 so
a+b+c+d+e=195
oldest is 13 older thatn youngest
e=13+a
middle child anne (c) is 5 years younger than josie who is an unknow position, we know that she could be d or e or oldest or second oldest
the other 2 are 6 years appart
b and d ar e 6 years appart or b and e are 6 years apart? or is josie the oldest, or second oldest?

second oldes is 42 so
d=42

2 scenarios
if josie is oldest, then see AAAA and if josie is second oldest then see BBBB

AAAA
josie is 13 years older than mark
e=13+a
anne is 5 less than josie
c=e-5
the other 2 are 6 years apart
b+6=d
d=42
subsitute and get
b=36
add and get
78+a+c+e=195
a+c+e=117
e-13+e-5+e=117
3e-18=117
add 18 to both sides
3e=135
divided both sides by 3
e=45
subsitute
a=32
b=36
c=40
d=42
e=45


BBBB
oldest is 13 older than youngest
e=13+a
middle is 5 younger than josie (d)
c=d-5
the other 2 are 6 apart
b=e-6
d=42
subsitute
c=37
subsitute
a+b+37+42+e=195
a+b+e+79=195
subtract 79 from both sides
a+b+e=116
subsitute
e-13+e-6+e=116
3e-19=116
add 19 to both sides
3e=135
divide both sides by 3
e=45
subsitute
45-6=39=b
45-13=32=a
c=42-5=37
this is wrong because b cannot be older than c so therefor AAA si the correct answer


THE ANSWER IS
Josie is the oldest=45
Unknown is second oldest=42
Anne is middle=40
Unknown2 is second youngest=36
Mark is the youngest=32

Answer 2

A is oldest, Josie, 45
B is second oldest, 42
C is middle, Anne, 40
D is second youngest, 36
E is youngest, Marc, 32
A+B+C+D+E=195
A-E=13 or E=A-13
A-C=5 or C=A-5
B-D=6
B=42 so D=36 so 195-B-D=117 so A+C+E=117
Plug in terms of A in for C and E so A+(A-5)+(A-13)=117
3A-18=117
3A=135
A=45 and to find C and E we just plug this A into those equations