Question 1035952: Joan and Jane are sisters. Jean is Joan's daughter and she is 12 years younger than her aunt. Joan is twice as old as Jean. Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece. How old is Jean?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Joan and Jane are sisters. Jean is Joan's daughter and she is 12 years younger than her aunt.
Joan is twice as old as Jean.
Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece.
How old is Jean?
:
The similarity of these names make it confusing, assign their names as follows
a = Joan's age
b = Jane's
c = Jean's
:
Write an equation for each statement
:
"Jean is Joan's daughter and she is 12 years younger than her aunt."
c = b - 12
"Joan is twice as old as Jean."
a = 2c
" Four years ago, Joan was the same age as Jane is now,"
a - 4 = b
a = b + 4
" and Jane was twice as old as her niece."
b - 4 = 2(c - 4)
simplify
b - 4 = 2c - 8
b = 2c - 8 + 4
b = 2c - 4
Using the 1st equation, replace c with (b-12)
b = 2(b-12) - 4
b = 2b - 24 - 4
b - 2b = -38
-b = -28
therefore
b = 28 yrs Jane's age
Find a
a = b + 4
a = 28 + 4
a = 32 is Joan's age
:
How old is Jean?
we know that a = 2c, therefore
32 = 2c
c = 32/2
c = 16 yrs is Jean's age
;
:
:
See if this checks out in the statement
" Four years ago, Joan was the same age as Jane is now,"
32 - 4 = 28
and Jane was twice as old as her niece. "
28 - 4 = 2(16 - 4)
24 = 2(12)
|
|
|
