Question 1194528: Hi there! I'm having trouble with this question, and I think it's just that I'm doubting the answer that I've gotten.
The question is:
A man is currently six times older than his granddaughter. Thirteen years ago, he was 18 times older than her. What are their current ages?
I set the problem out as such:
Let x = granddaughters age
Let y = mans age
so,
6x = y --------- (1)
y - 13 = 18(x - 13) --------- (2)
substituting (1) into (2):
6x - 13 = 18(x - 13)
12x = 221
x = 18.41666667
substituting this into (1)
6(18.41666667) = 110.5
so the mans age is 110.5, and the granddaughters age is 18.4666667
checking this:
thirteen years ago:
110.5 - 13 = 97.5
18.41666667 - 13 = 5.41666667
18(5.41666667) = 97.5
So the numbers check out, but only if you include all decimal points.
It seems like an incredibly dissatisfying answer!! Not to mention decimals such as this are difficult to translate into months of a year. Also, that man is INCREDIBLY old! I just can't shake the feeling that I've worked it out wrong.
even when shortening to 6(18.4) = 110.4
then 18(5.4) = 97.2 (which is only approximately 18 times their age)
or
or 6(18.42) = 110.52
then 18(5.52) = 97.56 (which is again only approximately 18 times her age)
Have I worked this question out incorrectly?? It seems unreasonable to have to keep so many decimal places, especially with a question of this type.
I would appreciate it if you can point out any flaws in my calculations, or your advice.
Thank you!
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The question is:
A man is currently six times older than his granddaughter. Thirteen years ago, he was 18 times older than her. What are their current ages?
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Ignoring the fact that 6 times older = 7 times as old, and 18 times older is 19 times as old:
=====
M = 6G
M-13 = 18*(G-13)
---
6G-13 = 18G - 234
12G = 221 **** not integers
=============
M = 7G
M-13 = 19*(G-13)
7G-13 = 19G - 247
12G = 234
G = 19.5 **** not integers
-----------------------------
Age problems usually accept only integers.
Answer by josgarithmetic(39616)  (Show Source):
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