Question 977269: Mrs. A has four children, namely, P, Q, R, and S. Q is currently twice the age of S. Two years ago, P was twice the age of R. Four years ago, Q was twice the age of R. Two years from now, P would be twice the age of S. Three years ago, R was twice the age of S. Mrs. A current age is the sum of her children's current age.
What are the current ages of Mrs. A and her children P, Q, R, & S.
Need help to form the equation to solve the problem.
Answer
p 12
q 10
r 7
s 5
A 34
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Mrs. A has four children, namely, P, Q, R, and S.
:
write an equation for each statement, simplify as much as possible
Q is currently twice the age of S.
q = 2s
Two years ago, P was twice the age of R.
p - 2 = 2(r-2)
p - 2 = 2r - 4
p = 2r - 4 + 2
p = 2r - 2
Four years ago, Q was twice the age of R.
q - 4 = 2(r-4)
q - 4 = 2r - 8
q = 2r - 8 + 4
q = 2r - 4
Two years from now, P would be twice the age of S.
p + 2 = 2(s+2)
p + 2 = 2s + 4
p = 2s + 4 - 2
p = 2s + 2
Three years ago, R was twice the age of S.
r - 3 = 2(s-3)
r - 3 = 2s - 6
r = 2s - 6 + 3
r = 2s - 3
Convert to s in terms r
-2s = -r - 3
same as
2s = r + 3
s = 
we also know that q = (2r-4)
Back to the 1st equation q = 2s, replace s and q
2r+4 = 2()
Cancel 2
2r - 4 = r + 3
2r - r = 3 + 4
r = 7
now you can replace r with 7 in the following equations and complete the problem
p = 2r - 2
q = 2r - 4
s =
:
Mrs. A current age is the sum of her children's current age.
A = p + q + r + s
What are the current ages of Mrs. A and her children P, Q, R, & S.
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