did you double post this? Seems there's two threads on this same topic started by the same OP at teh same time! Anyways, I've just copied and pasted the explanation I gave in the other thread. Hope it helps!
we have to translate the English into algebraic expressions that reflect the same meaning.
five years ago,Beth's age was three times that of Amy
How old is Beth today?...Let's call it "B"
Then, how old was Beth five years ago?..."B-5"
Similarly, how old was Amy five years ago?..."A-5"
At this point in time, Beth's age was three times that of Amy. So:
B-5 = 3*(A-5) (1)
Similarly, this sentence:
Ten years ago ,Beth's age was one half that of Chelsea.
B-10 = (C-10)/2 (2)
We want to solve for A in terms of C. So, we want to get rid of B. The easiest way is to equate the two equations. But the left-hand sides of each equation are different. So, just subtract 5 from both sides of (1) (OR add 5 to both sides of (2)):
B-5 -5 = 3*(A-5) - 5
B-10 = 3*(A-5) -5
Because B-10 = B-10, we have:
3*(A-5) - 5 = (C-10)/2
Solving for A, we have:
A = C/6 + 5
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