Question 1158669: Amy is four times older than James. Three years ago their ages combined was 54. How old is Amy
Found 3 solutions by josmiceli, Alan3354, ikleyn:
Answer by josmiceli(19441)   (Show Source):
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Amy is four times older than James.
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1 time older = an increase of 100% --> 2 times as old.
2 times older = an increase of 200% --> 3 times as old.
3 times older = an increase of 300% --> 4 times as old.
4 times older = an increase of 400% --> 5 times as old.
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4 times older is NOT the same as 4 times as old.
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Don't even think about "10 times smaller"
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people who don't understand math and science should not be submitting math problems.
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There's no voting about the solution of a math problem.
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Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
By standing on formal positions of the English language, I can (and I should) interpret the condition
as if Amy is 5 times as old as James
Let x = the James' age; then the Amy's age is 5x, according to my interpretation.
Then I can write this equation
(5x - 3) + (x-3) = 54
6x = 54 + 6 = 60
x = 60/6 = 10.
So, my answer is: Amy is 5*10 = 50 years.
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It is very difficult question: how to interpret.
Formally, English requires exactly this interpretation.
But, practically, in the everyday life, another interpretation just prevales.
The TRUTH is: in your mathematical composing and writing NEVER USE this form
"X is 4 times older than Y",
since it ALWAYS leads to confusing and misinterpretation.
Use this equivalent phrasing
"X is 5 times as old as Y".
instead. Then everybody will understand you by an UNIQUE WAY, and you will avoid misunderstanding.
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