FROM:
http://gmatclub.com/forum/mixture-probl ... ml#p544540
11. A certain type of concrete mixture is to be made of cement, sand and graved (gravel?) in a ratio 1:3:5 by weight. What is the greatest number of kilograms of this mixture that can be made with 5 kilograms of cement ?
1. 13 1/2
2. 15
3. 25
4. 40
5. 45
1:3:5
--> 1/9: 3/9: 5/9
--> 1/9(5) + 3/9(5) + 5/9 (5)
--> 5+15+25/9
--> 45/9
= 45
Please confirm and suggest any other method if possible
Thank you
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2 postsPage 1 of 1
- Deepak_J_Shah
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- RonPurewal
- Students
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- Joined: Tue Aug 14, 2007 8:23 am
Re: Mixture Problem: Need to verify Answer: Cement/Sand/Gravel
this is a weird question, because the prompt doesn't make sense.
since the problem states a fixed ratio of all the components, the outcome is COMPLETELY DETERMINED if any single one of those components is known. it therefore makes no sense to speak of the "greatest" amount of mixture that can be made with 5kg of cement, because, if we know there's 5kg of cement, then the ratio will tell us EXACTLY how much of EVERYTHING is in the mixture.
--
i also don't really understand your solution.
your CONVERSION OF RATIO TO FRACTIONS is entirely correct: the sum of 1, 3, and 5 is 9, so 9 becomes the denominator of all the fractions. Therefore, the fractional components of cement, sand, and gravel are 1/9, 3/9, and 5/9 respectively.
the first thing that's wrong is that you're apparently multiplying these numbers by 5. that doesn't make sense; the only thing by which you'd MULTIPLY these fractions is the TOTAL amount of mixture. i.e., the amount of cement is 1/9 times the total; the amount of sand is 3/9 times the total; and the amount of gravel is 5/9 times the total.
under no circumstances would you multiply 1/9, 3/9, or 5/9 by the amounts of the individual components.
remember, FRACTION x TOTAL AMOUNT = FRACTIONAL AMOUNT.
also, you appear to be dividing 45 by 9 and getting 45, which is ... interesting.
--
2 ways to do the problem:
(1) SOLVE FOR THE TOTAL
you've figured out that cement is 1/9 of the total.
therefore
CEMENT = (1/9)(TOTAL)
5 = (1/9)(TOTAL)
45 = TOTAL
(2) USE THE "X" MULTIPLIER
any three quantities in a 1:3:5 ratio can be expressed as x, 3x, and 5x, respectively.
therefore, cement = x
so, 5 = x
so, total = sum of all three = x + 3x + 5x = 9x
which = 9(5) = 45
since the problem states a fixed ratio of all the components, the outcome is COMPLETELY DETERMINED if any single one of those components is known. it therefore makes no sense to speak of the "greatest" amount of mixture that can be made with 5kg of cement, because, if we know there's 5kg of cement, then the ratio will tell us EXACTLY how much of EVERYTHING is in the mixture.
--
i also don't really understand your solution.
your CONVERSION OF RATIO TO FRACTIONS is entirely correct: the sum of 1, 3, and 5 is 9, so 9 becomes the denominator of all the fractions. Therefore, the fractional components of cement, sand, and gravel are 1/9, 3/9, and 5/9 respectively.
the first thing that's wrong is that you're apparently multiplying these numbers by 5. that doesn't make sense; the only thing by which you'd MULTIPLY these fractions is the TOTAL amount of mixture. i.e., the amount of cement is 1/9 times the total; the amount of sand is 3/9 times the total; and the amount of gravel is 5/9 times the total.
under no circumstances would you multiply 1/9, 3/9, or 5/9 by the amounts of the individual components.
remember, FRACTION x TOTAL AMOUNT = FRACTIONAL AMOUNT.
also, you appear to be dividing 45 by 9 and getting 45, which is ... interesting.
--
2 ways to do the problem:
(1) SOLVE FOR THE TOTAL
you've figured out that cement is 1/9 of the total.
therefore
CEMENT = (1/9)(TOTAL)
5 = (1/9)(TOTAL)
45 = TOTAL
(2) USE THE "X" MULTIPLIER
any three quantities in a 1:3:5 ratio can be expressed as x, 3x, and 5x, respectively.
therefore, cement = x
so, 5 = x
so, total = sum of all three = x + 3x + 5x = 9x
which = 9(5) = 45
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