SOLUTION: Matt, Rosa, and Kathy are cousins. If you combine their ages, they would be 40 years old. Matt is one-third of rosa's age. Kathy is five years older than rosa. How old are the thre

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Matt, Rosa, and Kathy are cousins. If you combine their ages, they would be 40 years old. Matt is one-third of rosa's age. Kathy is five years older than rosa. How old are the thre      Log On

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Question 1014815: Matt, Rosa, and Kathy are cousins. If you combine their ages, they would be 40 years old. Matt is one-third of rosa's age. Kathy is five years older than rosa. How old are the three cousins ?

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
m+r+k=40
m = r/3
k=r+5
The three equations imply, by direct substitution,
r/3 + r + (r+5) = 40
7r/3 = 35 after adding like terms and transposing the constant...
7r = 105 after cross-multiplication
r = 15
Meaning, Matt is 15/3 = 5 five years old, and Kathy is 15+5 = 20 years old.