SOLUTION: Sixteen year old Amelia is four times older than her brother Theodore. How old will Amelia be when she's twice as old?

Question 1198730: Sixteen year old Amelia is four times older than her brother Theodore. How old will Amelia be when she's twice as old?

Found 4 solutions by Theo, Alan3354, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
amelia is 16 years old
she is 4 times as old as her brother.
that means her brother is 4 years old.
amelia will be twice her age in 16 years.
her brother will then be 20.

that's what i get from the way the problem is stated.

you might have been asking how old amelia was when she is twice the age of her brother.
that's a different euqation.
we start with 16 = 4x, where x is the age of her brother.
that gets us x = 4, as before.
let y = the number of years before she becomes twice the age of her broher.
the equation for that is 16 + y = 2 * (4 + y)
simplify to get 16 + y = 8 + 2y
\subtract 8 from both sides of that equation and subtract y from both sides of that equation to get 16 - 8 = 2y - y\
simplify to get 8 = y
that says that she will be twice as old as her brother in 8 years.
she will be 24 and her brother will be 12.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
four times older = 5 times as old.
------
1 time older = 2x as old
2 times older = 3x as old
3 times older = 4x as old
etc
==================
"4 times older" is not as bad as "4 times closer" or "4 times colder"
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Sixteen year old Amelia is four times older than her brother Theodore.
How old will Amelia be when she's twice as old?
~~~~~~~~~~~~~~~~~~~

        The form " four times older than " is never used in Math problem written in English,
        since this form is ambiguous in English.

        The form " four times as old as " should be used in this problem in this context.

Amelia is 16; hence Theodore is 16/4 = 4. Let x be "in how many years". Write equation as you read the problem 16+x = 2*(4+x). Simplify and find x 16 + x = 8 + 2x 16 - 8 = 2x - x 8 = x ANSWER. In 8 years. Amelia will be 16+8 = 24 years old then.

Solved.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

As pointed out by some of the other tutors, the phrase "four times older than" should never be used in the statement of a math problem, because most people think it means something different than it really means.

If one person's age is x and another person is four times older than the first, then the age of the second person is x, PLUS 4 times x -- i.e., x+4x = 5x.

Unfortunately, in everyday usage, the phrase is used to mean that the age of the second person is 4x. But that is grammatically incorrect.

So in this problem the intended information is that Amelia is 4 times AS OLD AS her brother.

Then, since Amelia is 16, Theodore's age is 16/4 = 4. The difference in their ages is then 16-4 = 12 years.

Since the difference in their ages will always be 12 years, when Amelia is twice as old as Theodore she will be 24 and he will be 12.

ANSWER: 24

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