SOLUTION: Find the ages of Marry, George, Alice, Claire and Stephen if : Marry + George = 33 years between them Alice + Claire = 95 years between them Stephen + Marry= 72 years between

Question 1105782: Find the ages of Marry, George, Alice, Claire and Stephen if :
Marry + George = 33 years between them
Alice + Claire = 95 years between them
Stephen + Marry= 72 years between them
Marry + Claire = 87 years between them
Stephen + George = 73 years between them
plz Details solution of problem

Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

(1) M+G=33
(2) A+C=95
(3) S+M=72
(4) M+C=87
(5) S+G=73

Equations (1), (3), and (5) give the sums of the ages of Marry, George, and Stephen two at a time. So a quick path to the answer to the problem is to add those three equations:

(6)

Comparing (6) with (1), (3), and (5) shows that Marry is 16, George is 17, and Stephen is 56.
Then (4) tells us Claire is 71; and then (2) tells us Alice is 24.

Answers:
Marry 16
George 17
Alice 24
Claire 71
Stephen 56
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
You give a "+" and then said, "... years between them." This seems contradictory. If you mean SUM on both sides, then

Five linear equations in five unknown age variables. You can cut down to one equation in one variable through successive substitutions and simplifications.
-

-

Notice two equations sum of s and g, and difference of s and g.

Revise system:

Look at what is still unknown:

Last equation in that system:

The first substitution made was .

RESULTS
Marry, George, Alice, Claire and Stephen 16, 17, , , and 56

Alice should be 24 and Claire should be 71.

(Possible Mistake in Worked Steps)
RELATED QUESTIONS
If rose was four time younger than alice last year. And will be half the age of George... (answered by stanbon,ikleyn)
irene is 7 years younger than george, and george was twice as old as irene 6 years ago... (answered by ankor@dixie-net.com)
Kirstin is 4 times Claires age. Emily is 6 years older than Claire and 6 years younger... (answered by JBarnum)
the sum of claire's and hezron's ages are 50 years. in 2 1/2 years claire will be 5/6 of... (answered by sachi)
Kristen is 4 times Claire’s age. Emily is 6 times older than Claire and 6 years younger (answered by Alan3354,josgarithmetic)
) Kristen is four times as old as Claire. Emily is six years older than Claire and 6... (answered by josgarithmetic,MathTherapy)
Alice is ten years less than twice as old as Bonnie. If the sum of their ages is 26... (answered by CharlesG2)
George is 2 more than twice the age of alice. The product of their ages is 84. What are... (answered by lmeeks54)
Daphne is visited periodically by her three best friends: Alice, Beatrix and Claire.... (answered by KMST)