Question 240603: In three years, Lacey will be twice as old as Jennifer will be. At presemt, twice Lacey's age is the same as the product of Rachel's and Jennifer's ages. If Rachel is now twice as old as Jennifer, find the ages of all three girls.
I started out with let L be Lacey's age, J be Jennifer's age and R be Rachel's age. The first equation I came up with was (L+3)=2(J+3). The second was 2L=RJ. The 3rd was R=2J...
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! In three years, Lacey will be twice as old as Jennifer will be.
At present, twice Lacey's age is the same as the product of Rachel's and Jennifer's ages.
If Rachel is now twice as old as Jennifer, find the ages of all three girls.
:
Your equations are OK, just simplify the 1st one
:
The first equation I came up with was
(L+3)=2(J+3)
L + 3 = 2J + 6
L = 2J + 6 - 3
L = 2J + 3
:
The second was
2L = RJ
:
The 3rd was
R = 2J
:
Refer to the 1st equation, replace L in the 2nd equation with (2J+3)
2L = RJ
2(2J+3) = R*J
4J + 6 = R*J
:
Refer to the 3rd equation, replace R with 2J in the above equation
4J + 6 = 2J*J
4J + 6 = 2J^2
we can arrange this as a quadratic equation and solve
0 = 2J^2 - 4J - 6
Simplify divide by 2
0 = J^2 - 2J - 3
Factor this
(J-3)(J+1) = 0
The positive solution only
J = 3 yrs old is Jennifer's age
:
We can use your 3rd equation to find R
R = 2(3)
R = 6 yrs is Rachel's age
:
Find L using your 1st equation
L = 2J+3
L = 2(3) + 3
L = 9 yrs is Lacey's age
;
:
Check solution in the statement:
"In three years, Lacey will be twice as old as Jennifer will be."
9 + 3 = 2(3+3)
:
Also
"twice Lacey's age is the same as the product of Rachel's and Jennifer's ages"
2(9) = 6 * 3
;
Could you follow this OK? You made a good start.
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