Question 572761: jan is twice as old as jake. the sum of their ages is 5 less than twice of Jan's age. How old are jane ane jake?
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! Too bad they didn't have different initials or we could use those for our variable names. Instead, let's use X and Y.
Jan's current age = X
Jake's current age = Y
Jan is twice as old as Jake:
X = 2Y
The sum of their ages (X + Y) is 5 less than twice Jan's age (2X)
(X + Y) + 5 = 2X
Let's substitute for X in the above equation using X=2Y from before:
((2Y) + Y) + 5 = 2(2Y) We can remove the parens from the left side since it's all addition:
2Y + Y + 5 = 2(2Y)
combining terms:
3Y + 5 = 4Y
Subtract 3Y from both sides:
5 = Y
Jake is 5. Since Jan is twice Jake's age, she's 10.
Checking our answer:
The sum of their ages (5 + 10 = 15) is 5 less than twice Jan's age (20).
15 is 5 less than 20.
15 = 20 - 5
15 = 15 Correct!
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