|
Question 1152231: There is a mountain with 45 bat caves in a row .Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a row contain exactly 77 bats . Suppose the first cave has 7 times more bats than the last cave . What is the greatest possible number is bats in the second cave ?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52884)   (Show Source):
You can put this solution on YOUR website! .
In English, there is NO such phrase "7 times more . . . than".
My statement LITERALLY MEANS that these words do mean NOTHING in English;
so the entire post and the entire problem MAKE NO SENSE.
I understand that you translate from other language, but posting to this forum, it is YOUR RESPONSIBILITY and YOUR DUTY
to provide a correct, precise and non-ambiguous formulation/input.
Have a nice day (!)
===============
By the way, for the similar problem, see my post and my notice to your formulation at this link
https://www.algebra.com/algebra/homework/Average/Average.faq.question.1152153.html
https://www.algebra.com/algebra/homework/Average/Average.faq.question.1152153.html
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
The statement "the first cave has 7 times more bats than the last cave" DOES have a meaning in English -- but it is not the meaning that most people think.
"seven times AS MANY AS x" clearly means 7x. But "seven times MORE THAN x" means x, plus 7 more times x -- that is, x+7x = 8x, or 8 times x.
So we can work this problem logically, but we don't know the "right" answer, because we don't know whether the author of the problem meant the first cave has 7 times as many bats, or 8 times as many, as the last.
There are 45 caves, with at least 2 bats in each cave; and any 7 caves in a row contain exactly 77 bats. Given those conditions, the numbers of bats in successive caves must follow a repeating pattern, like this...:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 36 37 38 39 40 41 42 43 44 45
a b c d e f g a b c d e f g ... a b c d e f g a b c
The number of bats in caves 1 through 42 is 6*77 = 462. Since the total number of bats is 490, the number of bats in caves 43 to 45 (a+b+c) must be 490-462 = 28.
And that is the total number of bats in caves 1 to 3.
If we take the given information to mean that a is 7 times as much as c, then we have
a = 7c
a+b+c = 28
7c+b+c = 28
b = 28-8c
Then, given that the minimum number of bats in each cave is 2, the largest possible number of bats in the second cave is b = 28-16 = 12.
If the intended meaning of the given information was that a is 8 times as much as c, then we only have to modify those last calculations:
a = 8c
a+b+c = 28
8c+b+c = 28
b = 28-9c
Then the maximum number of bats in the second cave would be 28-18 = 10.
----------------------------------------------------------
It's unfortunate that the problem was worded exactly like this on a math contest problem.
In everyday usage, "seven times more than x" and "seven times as much as x" are carelessly used to mean the same thing, although grammatically they mean different things.
The ambiguous meaning of "x times more than..." makes its use inappropriate in a problem on a math contest. Note that I have even seen the phrase used on a problem on a practice SAT test. I would think writers of problems for practice SAT test would know it is inappropriate.
If you are ever in a math contest where disputes are allowed, then ALWAYS dispute any problem that uses the phrase "x times more than...". It is very likely that the right answer according to the person who wrote the problem is the grammatically wrong answer....
|
|
|
| |
