SOLUTION: If the sum of ages of three friends is 126.The ratio of ages of John and Maria is 4:3 and that of John and Linda is 5:7.Find the age of John?

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Question 357125: If the sum of ages of three friends is 126.The ratio of ages of John and Maria is 4:3 and that of John and Linda is 5:7.Find the age of John?
Answer by checkley77(12844) About Me  (Show Source):
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LET X=JOHN'S AGE
LET Y=MARIA'S AGE
LET Z=LINDA'S AGE.
X/Y=4/3
4Y=3X
Y=3X/4
X/Z=5/7
5Z=7X
Z=7X/5
X+Y+Z=126
X+(3X/4)+(7X/5)=126
(20X+5*3X+4*7X)/4*5=126
(20X+15X+28X)/20=126
63X=20*126
63X=2,250
X=2,520/63
X=40 AGE OF JOHN.
4Y=3*40
4Y=120
Y=120/40=30 AGE OF MARIA.
5Z=7*40
5Z=280
Z=280/5=56 AGE OF LINDA.
PROOF:
40+30+56=126
126=126