SOLUTION: How many years will it take for Sheila (34 years old) to be half the age of David (54 years old)?

Question 101024: How many years will it take for Sheila (34 years old) to be half the age of David (54 years old)?
Found 2 solutions by scott8148, bucky:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
unless they can travel back in time, never

she is already MORE THAN half his age and they are aging at the same rate
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
In x more years, Sheila will be 34 + x years old, and David will be 54 + x years old.
.
But the problem tells you that you want Sheila's age at that time to equal half of David's age.
So write an equation that says Sheila's age of 34 + x equals (1/2) times David's age of 54 + x:
.
34 + x = (1/2)* (54 + x)
.
To get rid of the (1/2) just multiply both sides of the equation by 2 and you have:
.
68 + 2x = 54 + x
.
get rid of the x on the right side by subtracting x from both sides to get:
.
68 + x = 54
.
Next, get rid of the 68 on the left side by subtracting 68 from both sides to result in:
.
x = -14
.
What does this negative answer mean? It means that you are too late. 14 years ago when
Sheila was 20 (that is 34 - 14 = 20), she was half the age of David who was then 40 (54 - 14 = 40).
That ratio can never happen again. Somebody was trying to trick you or to see if you even
recognized what the answer meant.
.
You can try adding some years to Sheila's present age of 34 and add the same number of years
to David's present age of 54. You will see that the ratio of Sheila's age to David's age
just keeps getting bigger and bigger than 1/2. For example, in 10 years Sheila will be 44
and David will be 64. The ratio of 44 to 64 equals 44/64 and the decimal equivalent
is 0.6875. In 20 years Sheila will be 54 and David will be 74. This ratio is 54/74 and
the decimal equivalent is 0.7297. In 30 years Sheila will be 64 and David will be 84, a
ratio of 64/84 which is 0.7619. Do you see how with every passing year the ratio keeps growing
away from 1/2 which is 0.5000?
.
Hope this helps you to interpret the problem a little better.
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