Jean is 16.
Let x represent Joan's age. Let y represent Jane's age. Let z represent
Jean is Joan's daughter and she is 12 years younger than her aunt.
So z = y - 12.
Joan is twice as old as Jean.
So x = 2z.
Four years ago, Joan was the same age as Jane is now, and Jane was twice as
old as her niece.
So x - 4 = y and y - 4 = 2(z - 4).
If we solve the last equation for y we can substitute that value of y into the
first equation to solve for z.
y - 4 = 2(z - 4)
y - 4 = 2z - 8
y = 2z - 4
Now substitute this value for y into the first equation.
z = y - 12
z = 2z - 4 - 12
z = 2z -16
z = 16
We didn't use any information about Joan's age to solve the problem, so let
solve all the ages to make sure we have the right answer.
z = 16 Jean (12 years younger than Jane.)
x = 2z so x = 32 Joan (Twice as old as Jean and four
years ago same age as Jane is now.)
x - 4 = y so y = 28 Jane (Four years ago she was
twice the age of Jean.)
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