SOLUTION: Mary, Jane and Gloria are sisters. Mary is one year younger than the sum of janes and Gloria's ages. Jane is eight years older than Gloria and all together they are 35 years old. F

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Question 889873: Mary, Jane and Gloria are sisters. Mary is one year younger than the sum of janes and Gloria's ages. Jane is eight years older than Gloria and all together they are 35 years old. Find how old are the sisters
Answer by JulietG(1812) About Me  (Show Source):
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M = J + G - 1
J = G + 8
M + J + G = 35
Substitute the value of M from the first equation into the bottom equation
M + J + G = 35
(J+G-1) + J + G = 35
Substitute the value of J above into the new equation
(J+G-1) + J + G = 35
(G+8)+G-1 + (G+8) + G = 35
Add
4G + 15 = 35
Subtract 15 from each side
4G = 20
Divide each side by 4
G = 5
If Gloria is 5, then Jane is 13. [ Jane is eight years older than Gloria]
If Gloria is 5 and Jane is 13, then Mary is 17 [Mary is one year younger than the sum of janes and Gloria's ages]
Add their ages -- 5 + 13 + 17 = 35
Success!