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?
(A) \(13\frac12\)
(B) \(15\)
(C) \(25\)
(D) \(40\)
(E) \(45\)
[spoiler]OA=E[/spoiler]
Source: Official Guide
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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
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We are given that cement, sand, and gravel are in a ratio 1:3:5, which means every 1 kg of cement needs a 3kg of sand and 5 kg of gravel, or vice verse. And we want to know what is the greatest number of kilograms of this mixture can be made with 5 kilograms of cement.
We have 5kg of cement and we want to know what x and y are
$$\frac{1\ cement\ :\ 3\ sand:\ 5\ gravel}{5:\ x:\ y}$$
Notice that cement is multiplied by 5, we can do the same thing for sand and gravel to get the portion needed for this mixture. And it gives us this $$\frac{1\ cement\ :\ 3\ sand:\ 5\ gravel}{5\ cement\ :\ 15\ sand\ :\ 25\ gravel}$$
Add it all up: 5 + 15 + 25 = 45
Answer: E
We have 5kg of cement and we want to know what x and y are
$$\frac{1\ cement\ :\ 3\ sand:\ 5\ gravel}{5:\ x:\ y}$$
Notice that cement is multiplied by 5, we can do the same thing for sand and gravel to get the portion needed for this mixture. And it gives us this $$\frac{1\ cement\ :\ 3\ sand:\ 5\ gravel}{5\ cement\ :\ 15\ sand\ :\ 25\ gravel}$$
Add it all up: 5 + 15 + 25 = 45
Answer: E
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Jay@ManhattanReview
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So, we are given that the ratio of cement, sand, and gravel is 1:3:5 and the available quantity of cement is 5 kg.Vincen wrote: ↑Tue Jun 02, 2020 7:52 amA 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?
(A) \(13\frac12\)
(B) \(15\)
(C) \(25\)
(D) \(40\)
(E) \(45\)
[spoiler]OA=E[/spoiler]
Source: Official Guide
From the ratio 1:3:5, we find that from 1 kg cement, 1 + 3 + 5 = 9 kg. mixture can be made.
Thus, from 5 kg cement, 5*9 = 45 kg. mixture can be made.
The correct answer: E
Hope this helps!
-Jay
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quichopipe
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We know that the ration is as follows:
C:S:G
1:3:5
We are told that there are 5kg of cement. That means that the ratio is multiplied by 5 (1*5 = 5); therefore, we must multiply every number by 5.
The new ratio becomes
C:S:G
5:15:25
And so 5+15+25 = 45.
Answer choice E
C:S:G
1:3:5
We are told that there are 5kg of cement. That means that the ratio is multiplied by 5 (1*5 = 5); therefore, we must multiply every number by 5.
The new ratio becomes
C:S:G
5:15:25
And so 5+15+25 = 45.
Answer choice E
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Scott@TargetTestPrep
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Solution:Vincen wrote: ↑Tue Jun 02, 2020 7:52 amA 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?
(A) \(13\frac12\)
(B) \(15\)
(C) \(25\)
(D) \(40\)
(E) \(45\)
[spoiler]OA=E[/spoiler]
Source: Official Guide
If there are 5 kg of cement, there will be 5 x 3 = 15 kg of sand and 5 x 5 = 25 kg of gravel. Therefore, there are 5 + 15 + 25 = 45 kg of the mixture.
Answer: E
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