SOLUTION: Edwin is 6 years older than his brother Alvin. In two years, Edwin will be 20 more than one-third of Alvin's age. How old are the brothers now?

Question 123895: Edwin is 6 years older than his brother Alvin. In two years, Edwin will be 20 more than one-third of Alvin's age. How old are the brothers now?
Found 2 solutions by applesrbest, bucky:
Answer by applesrbest(7) (Show Source): You can put this solution on YOUR website!
Let Alvin's age now be x, and Edwin's age be x+6.
Therefore, in 2 years' time,
x+8 = (1/3)(x+2) + 20
x+8 = (1/3)(x) + 62/3
(2/3)x = 38/3
x = 19
Hence, Alvin is 19 years old, and Edwin is x+6 = 19+6 = 25

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let E represent Edwin's present age and A represent Alvin's present age.
.
The problem tells you first that presently Edwin is 6 years older than his brother Alvin. That
means that if you take 6 years off Edwin's present age, the answer you get is equal to
Alvin's present age. In equation form this is:
.
E - 6 = A
.
Next the problem indicates what the relationship between their ages will be 2 years from now.
In two years from now Edwin's age will be his present age plus 2 ... or E + 2. And also in 2 years
from now Alvin's age will be his present age plus 2 ... or A + 2.
.
The problem then tells you that 2 years from now Edwin's age at that time will be 20 more than
a third of Alvin's age. This tells you that if you take 20 years away from Edwin's
age at that time the answer will equal a third of Alvin's age at that time.
.
Well, 20 years off Edwin's age in 2 years will be (E + 2) - 20 and this simplifies
to E - 18.
.
And a third of Alvin's age in 2 years will be
.
Since we know these two are to be equal, we can set them equal in the equation form of:
.

.
We can get rid of the denominator 3 by multiplying both sides of this equation by 3 to
convert the equation to:
.

.
But way back at the start our first equation said that E - 6 = A. So wherever we see A we can
substitute it equal E - 6. Substituting E-6 for A in the equation above results in the equation becoming:
.

.
Combine the constants -6 and +2 on the right side to get -4 which reduces the equation to:
.

.
Get rid of the -54 on the left side by adding +54 to both sides and the equation becomes:
.

.
Get rid of the E on the right side by subtracting E from both sides to get:
.

.
Solve for E by dividing both sides by 2 and you have:
.

.
So Edwin's present age is 25. And since Edwin is 6 years older than Alvin, then Alvin's present
age is 25 - 6 = 19 years old.
.
In two years from the present, Edwin will be 27 and Alvin will be 21. (Still 6 years difference
in their ages, just as there will always be.)
.
If you took 20 from Edwin's age of 27 you get an answer of 7. And if you took a third of
Alvin's age of 21 you also get an answer of 7. So our answer satisfies both of the sets of
conditions given in the problem.
.
In summary, the answer to this problem is that Edwin is currently 25 years old and Alvin is
currently 19 years old.
.
Hope all this helps you to understand the problem and how to work it.
.

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