Question 30227: I'm such a dunce with Math that I'm not even sure if my question is an equation. I have the following word problem.
Rick is 6 years older than Nick. In 4 years he will be twice as old as Nick. In 10 years Nick will be 2/3 Rick's age. How old are each of them?
By trial and error I solved the problem as 8 & 2. I can present the problem as x = y + 4,
x + 4 = y + 4 + 4, and
(x + 10)* 2 = (y + 10)* 3
Is there a mathmatical way to solve this?
Found 3 solutions by Fermat, Paul, atif.muhammad:
Answer by Fermat(136)   (Show Source):
You can put this solution on YOUR website! Let R represent the age of Rick.
Let N represent the age of Nick.
Rick is 6 years older than Nick: this becomes,
R = N + 6 -----------------------------------------(1)
In 4 years he (Rick) will be twice as old as Nick: this becomes
R+4 = 2*(N+4) ------------------------------------(2)
From (1), substitute for R = N + 6 into (2), giving
N+6 + 4 = 2N + 8
6+4-8 = 2N - N
N = 2
=====
R = N+6
R = 8
=====
You only really need the two statements. The third one is redundant. But you can use it to check out your answer.
In 10 years Nick will be 2/3 Rick's age: this becomes
N + 10 = (2/3)(R + 10)
2 + 10 =(2/3)(18)
12 = 12
lhs = rhs - ans checks out :)
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Answer by Paul(988)  (Show Source):
Answer by atif.muhammad(135) (Show Source):
You can put this solution on YOUR website! Now:
Nick's age = x yrs
Rick is 6 years old than Nick so his age is (x+6) yrs
In 4 years:
Rick's age now will be (x+6) +4 = (x+10) yrs
Nick's age = (x+4) yrs
In 4 yrs, Rick will be twice as old as Nick, therefore: (x+10) = 2(x+4)
In 10 years:
Nick's age = (x+10) yrs
Rick's age = (x+6) + 10 = (x+16) yrs
Nick is now 2/3 of Rick therefore, 3(x+10)/2 = (x+16)
We now have two equations:
(x+10) = 2(x+4)
(x+10) = 2x +8
10 - 8 = 2x - x
2 = x
x = 2
Nick is 2 yrs old
We know that Rick is (x+6) yrs old therefore, Rick is (2+6) yrs old = 8 yrs old
3(x+10)/2 = (x+16)
We don't need to even bother about this equation as we have already found out our answer.
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