SOLUTION: David is 30 years younger than his father. Two years ago, 3 times of David's age was 20 years older than half that of his father. How old is David now? Let x be David's age now.

Algebra ->  Finance -> SOLUTION: David is 30 years younger than his father. Two years ago, 3 times of David's age was 20 years older than half that of his father. How old is David now? Let x be David's age now.      Log On


   

Question 1100302: David is 30 years younger than his father. Two years ago, 3 times of David's age was 20 years older than half that of his father. How old is David now?
Let x be David's age now.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = dave's age now.

dave's father's age now is therefore x + 30

2 year's ago, dave's age was (x-2).

2 year's ago, dave's father's age was (x-2) + 30 = x + 28

2 years's ago, 3 times dave's age then was 20 more than half of his father's age then.

3 * (x-2) = 1/2 * (x + 28) + 20

simplify this to get:

3x - 6 = 1/2 * x + 14 + 20

combine like terms to get:

3x - 6 = 1/2 * x + 34

subtract 1/2 * x from both sides of this equation and add 6 to both sides of this equation to get:

3x - 1/2 * x = 40

combine like terms to get:

2.5 * x = 40

solve for x to get x = 40 / 2.5 = 16

that's dave's age today.
his father's age today is 46

2 years ago:

dave was 14
his father was 44

3 * 14 = 42
1/2 * 44 + 20 = 22 + 20 = 42

3 times dave's age 2 years ago is equal to 20 more than half dave's father's age 2 years ago.

solution looks good.

solution is dave's age today is 16.