Question 206338: Dot and her cousin have a combined age of 24 years, 3 years ago, dot was exactly twice as old as her cousin. How old is dot now?
Answer by mickclns(59)   (Show Source):
You can put this solution on YOUR website! d is Dot's age now, c is cousin's age now -- don't just say d=Dot. Dot isn't a number, don't just say Dot's age, because there is more than one age for Dot in this problem. It is amazing how many students have trouble with translating the English into the math, simply because they aren't clear to themselves what the variables stand for (so often confuse them). So:
d is Dot's age now, c is cousin's age now, d-3 was Dot's age 3 years ago, c-3 was cousin's age 3 years ago
Now translate directly into math:
d + c = 24
d-3 = 2(c-3) --> d-3 = 2c - 6 --> d = 2c - 3
Since you want to find how old dot is now, that is, d, solve for c in terms of d and substitute:
c = 24 - d (substitute into equation at end of line second above)
d = 2(24 - d) - 3 --> d = 48 - 2d - 3 --> 3d = 45 --> d=15 your answer (find c and check in word problem)
Alternatively you could have used one variable d (since that is what you're looking for).
d is Dot's age now, 24 - d is cousin's age now, d-3 was Dot's age 3 years ago, (24 - d) -3 = 21 - d was cousin's age 3 years ago. Then you would only have one equation to solve since you used the fact that their combined age now is 24 to find 24 - d as the cousin's age now. That one equation is:
d-3 = 2(21 - d) --> d-3 = 42 - 2d --> 3d = 45 --> d = 15.
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