Question: Can you answer this Simple math mind game problem?

Noah and Hannah together are 21 years old. Noah and Karen are 54 years old while Hannah and Karen are 51 years old together. How old is each person?

Relation Questions:

Let n be Noah's age
h be Hannah's age and
k be Karen's age
n+h = 21 ....eq1
n+k = 54 ...eq2
h+k = 51 ...eq3
subtracting eq3 from eq2
n-h = 3 i.e n = h+3
sustituting for n in eq1
h+3+h= 21 i.e. 2h+3 =21 or 2h = 18 and so h = 9
n= h+3 i.e n = 9+3 = 12
substituting for n in eq2
12+k = 54 i.e. k = 54-12 = 42
or
substituting for h in eq3
9+k=51 i.e k= 51-9 = 42
Hanah's is 9 years old
Noah's is 12 years old
Karen's is 42 years old

Noah is 12
Hannah is 9
Karen is 42

:)

Noah, x
Hannah, y
Karen, z

x + y = 21 ------Eq 1
x + z = 54 ------ Eq 2
y + z = 51 ------ Eq 3

eq 1 - eq 2

x + z - y - z = 54 - 51
x - y = 3 ----- Eq 4

Eq 1 + eq 2

x + y + x - y = 21 + 3
2x = 24
x = 12 (Noah)

Sub into eq 1
12 + y = 21
y = 9 (Hannah)

sub into eq 2
9 + z = 51
z = 42(karen)

noah age is n

hannah age is h

karen age is k

(1) n + h = 21
(2) n+k = 54
(3) h+k = 51

now we compute (1) - (2) - (3), i.e.

-2k = - 84
k = 42.

karen's age is 42. so hannah's age then becomes 9 and noah's age becomes 12

daniel and granda are over-doing it. Its an overkill. It just needs 1 computation ONLY to find karen's age.