Question 185872: Mary, who is sixteen years old, is four times as old as her brother. How old will Mary be when she is twice as old as her brother?
Found 2 solutions by feliz1965, Fals:
Answer by feliz1965(151)   (Show Source):
You can put this solution on YOUR website! Mary, who is sixteen years old, is four times as old as her brother. How old will Mary be when she is twice as old as her brother?
If Mary is 16 and this is 4 times as old as her brother, then we can say that her brother is 4 years old.
Let M = Mary's age when she is 2x as old as her brother.
16/M = 4/8
4M = 128
M = 128/4
M = 32
Answer by Fals(5)  (Show Source):
You can put this solution on YOUR website! I'm afraid feliz1965 is wrong and it makes absolutely no sense to put an 8 in "16/M = 4/8" or to even use that equation at all. If Mary was 32 years old as feliz says, then her brother would be 20 years old... 32 is not twice as old as 20.
The correct answer is 24. Mary will be 24 years old when she is twice the age of her brother (which will be 12).
First, find the age of her brother when she is 16 years old:
16=4x
Divide both sides by 4:
4=x
So Mary is 16 and her brother is 4.
Now we move onto the part where it asks how old Mary will be when she is twice as old as her brother:
16+x=2(4+x)
If you don't understand why I am using that equation, it is because we are trying to find out how many years it will take for Mary to be twice as old as her brother. Each year Mary and her brother grow one year older. So whenever you add a year to Mary (x) you must also add a year to her brother (x). We already know that Mary is 16 years old, and her brother is 4 years old. We use 2(4+x) because we're looking for Mary's age when she is "twice" as old as her brother.
16+x=2(4+x)
Multiply the 2 by the 4 and the x:
16+x=8+2x
Subtract 8 from both sides:
8+x=2x
Subtract x from both sides:
8=x
So now we know that in 8 years from Mary's current age (16) she will be twice as old as her brother (who will also be 8 years older from his current age, which is 4). So now that we know x=8 we'll use the same equation we started with and plug the 8 in where x is:
16+x=2(4+x)
16+8=2(4+8)
Sixteen plus eight equals 24, and four plus eight equals 12.
24=2(12)
So now we can already see that 24 is twice as old as 12.
Multiply 2 by 12:
24=24
In eight years Mary will be 24 and her brother will be 12. She will be twice as old as her brother when she is 24 years old.
16+8=24
4+8=12
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