SOLUTION: Beth is 4 years older than Jane. Sally is twice as old as Jane. Bill is twice as old as Sally. If the sum of their ages is 84 how old is each person?

Question 916859: Beth is 4 years older than Jane. Sally is twice as old as Jane. Bill is twice as old as Sally. If the sum of their ages is 84 how old is each person?
Found 2 solutions by DrBeeee, stanbon:
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let
B = Beth's age
J = Jane's age
S = Sally's age
W = Bill's age
The problem statement gives us the four equations:
(1) B = J + 4
(2) S = 2*J
(3) W = 2*S = 4*J
(4) B+J+S+W = 84 or
(5) J +4 +J + 2*J + 4*J = 84 or
(6) 8*J = 80 or
(7) J = 10
Then
(8) B = 14 and
(9) S = 20 and
(10) W = 40
Check this with (5)
Is (14+10+20+40=84)?
Is (84=84)? Yes
Answer: Beth is 14, Jane is 10, Sally is 20 and Bill is 40.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Beth is 4 years older than Jane. Sally is twice as old as Jane. Bill is twice as old as Sally. If the sum of their ages is 84 how old is each person?
==============
Equations:
b = j + 4
s = 2j
b = 2s
------
b + j + s = 84
---
Substitute:
j+4 + j + (b/2) = 84
Substitute:
2j + 4 + (j+4)/2 = 84
------
4j + 8 + j+4 = 168
5j = 156
----
j = 31 1/5 (jane's age)
b = j+4 = 35 1/5 (Beth's age)
s = b/2 = 78/5 = 17 3/5 (Sally's age now)
-----------------------
Cheers,
Stan H.
================
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