Question 568337: Can you please help me with this problem? "Six years ago, Josie was 5 times as old as her niece, Dianne. How old is Dianne now if her age is one-third that of her aunt's.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the aunt's age.
let y equal the niece's age.
the niece is currently 1/3 the age of the aunt.
the equation for that is:
y = x/3
if we solve this equation for x, we get:
x = 3y
6 years ago the aunt's age was 5 times the niece's age.
the equation for that is:
x - 6 = 5 * (y - 6)
since we have y = x/3 and we have the equivalent equation of x = 3y, we can substitute either in the equation of x - 6 = 5 * (y - 6) to eliminate one of the unknowns in that equation.
we'll use x = 3y because it seems to make the calculations easier.
the equation of:
x - 6 = 5 * (y - 6) becomes:
3y - 6 = 5 * (y - 6)
simplify this to get:
3y - 6 = 5y - 30
subtract 3y from both sides of this equation and add 30 to both sides of this equation to get:
24 = 2y
divide both sides of this equation by 2 to get:
12 = y which is the same as:
y = 12
since x = 3y, this makes x = 36
x is the aunt's age.
y is the niece's age.
the aunt is 36 years old today.
the niece is 12 years old today.
6 years ago the aunt was 30.
6 years ago the niece was 6.
6 years ago the aunt was 5 times as old as the niece.
today the niece is 1/3 as old as the aunt.
it all checks out, so the answer is:
josie is 36 years old.
dianne is 12 years old.
josie is the aunt.
dianne is the niece.
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