Cory is 6 years older than her sister.Four years ago, she was 4 times as old her sister.how old is cory now?
let c = cory's age now
let s = her sisters age now
cory's age now = sisters age + 6 years
=> c = s + 6
4 years ago, cory was 4 years younger ( i.e. c-4) and her sister was 4 years younger (s- 4)
4 years ago cory was 4 times older than her sister
=> c - 4 = 4*(s-4)
We can simplify this to
c = 4s - 16 +4
c = 4s - 12
We can then use simultaneous equations to solve the two equations
(i) c = s + 6
(ii) c = 4s - 12
If we multiply both sides of equation (i) by 4 we get
(iii) 4c = 4s + 24
We can then subtract equation (ii) from equation (iii) to eliminate the '4s' term
=> ( 4c = 4s + 24 ) - (c = 4s - 12)
=> 4c - c = 4s +24 - 4s +12
=> 3c = 4s - 4s +36
=> 3c = 36
=> c = 36/3
=> c = 12
=> Cory's age now = 12
Her sister's age now is of course 6
4 years ago Cory would of been 8 and her sister would of been 2
I hope this helps and good luck! If you have more questions - ask away!
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Many Thanks Don.
Sep 13, 2011 |
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