Question 251591: Eight years ago, Ed was ten times as old as his youngest daughter Faith. In six years, he will only be three times as old as her. What are Ed's and Faith's ages now?
I needed a system of two equations and I came up with
10F-8=E-8
3F+6=E+6
They didn't work. I'm terrible with age problems. Please help!
Found 5 solutions by richwmiller, AndrewWillie, josgarithmetic, ikleyn, greenestamps:
Answer by richwmiller(17219)   (Show Source):
Answer by AndrewWillie(2)  (Show Source):
Answer by josgarithmetic(39617)  (Show Source):
You can put this solution on YOUR website! x, Faith
y, Ed
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Eight years ago, Ed was ten times as old as his youngest daughter Faith.
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In six years, he will only be three times as old as her.
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Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
Let x be the daughter's age now, and let y be the Ed's age.
Eight years ago, the daughter was (x-8) years old;
Ed was (y-8) years old.
So, your first equation is
y - 8 = 10*(x-8). (1)
In six years, Ed will be (y+6) years old;
his daughter will be (x+6) years old.
So, your second equation is
y + 6 = 3*(x+6). (2)
Now our task is to solve equations (1) and (2).
For it, express y from equation (1)
y = 10*(x-8) + 8 = 10x - 80 + 8 = 10x - 72 (3)
and substitute it into equation (2). You will get
10x - 72 + 6 = 3x + 18
10x - 3x = 18 + 72 - 6
7x = 84
x = 84/7 = 12.
Thus the daughter is 12 years old now.
Then the father is, according to (3), 10x - 72 = 10*12 - 72 = 120 - 72 = 48 years old.
Solved.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
It's obvious from the work you show that you have....
F = Faith's age
E = Ed's age
F-8 = Faith's age 8 years ago
E-8 = Ed's age 8 years ago
F+6 = Faith's age 6 years from now
E+6 = Ed's age 6 years from now
The work you have done there -- coming up with the expressions representing their ages 8 years ago and 6 years from now -- was exactly right. So you have an excellent start on solving the problem.
So let's look at why your equations didn't get you to the solution to the problem.
Let's re-phrase the given information using the language of equations. Then we will look at how to use the expressions you have to write those equations, and we will compare that to the equations you wrote.
(1) Ten times Faith's age eight years ago was equal to Ed's age eight years ago.
Ed's age 8 years ago was E-8; Faith's age 8 years ago was F-8. 10 times Faith's age 8 years ago is then 10(F-8). So the equation should be
10(F-8) = E-8
Your equation was
10F-8 = E-8
Do you see that the expression on the left side of your equation does NOT say "10 times Faith's age 8 years ago"?
So your mistake was the simple one of not using parentheses where required to make the equation say what you meant it to say.
So, with the good start you had, I think that, with just a little more care to make sure your equations say what you mean for them to say, you will do okay with solving these kinds of problems.
(2) Three times Faith's age six years from now will be Ed's age six years from now.
I hope you see that your mistake here is exactly the same thing. The left side of your second equation does NOT represent "3 times Faith's age 6 years from now". That left side of that equation has to be 3(F+6) -- not just "3F+6".
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