SOLUTION: Elvin is 2 more than three times older than his daughter, Ezra. In 16 years, he will be twice as old as his daughter. What are their present ages?

Question 1176790: Elvin is 2 more than three times older than his daughter, Ezra. In 16 years, he will be twice as old as his daughter. What are their present ages?

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

let Elvin's age be and Ezra 's age be
if Elvin is than older than his daughter, Ezra, we have
.....eq.1
In years, he will be as old as his daughter, so we have

.....eq.2
from eq.1 and eq.2 we have

go to
.....eq.1, substitute

their present ages:
Elvin is and Ezra is

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I have no doubt that the solution by the other tutor is the solution the author of the problem intended. However, the answer is different if the problem is solved EXACTLY as written.

The problem is the use of the phrase "2 more than 3 times older than".

If Ezra's age is x, then 2 more than 3 times OLDER THAN x is 2 more than (x plus 3 times x), or 2 more than 4x, which is 4x+2.

On the other hand, if Ezra's age is x, then 2 more than 3 times AS OLD AS x is 2 more than 3x, which is 3x+2.

Unfortunately, in everyday usage, the phrases "3 times AS OLD AS" and "3 times OLDER THAN" are sloppily used to mean the same thing.

So the grammatically correct interpretation of the given information is that if Ezra's age is x then Elvin's age is 4x+2, NOT 3x+2. So....

Let x = Ezra's age
Then 4x+2 = Elvin's age

Then

x+16 = Ezra's age in 16 years
4x+18 = Elvin's age in 16 years

In 16 years, Elvin's age will be twice Ezra's age:

ANSWER: their current ages are x=7 and 4x+2=30

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