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If a certain concrete mixture contains gravel, water, and sand in a 1

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If a certain concrete mixture contains gravel, water, and sand in a 1  [#permalink]

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New post 14 Sep 2018, 11:29
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If a certain concrete mixture contains gravel, water, and sand in a 1 to 3 to 5 ratio by weight, how many pounds of gravel would be needed to produce 72 pounds of the mixture?

1. 72

2. 40

3. 24

4. 9

5. 8

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Re: If a certain concrete mixture contains gravel, water, and sand in a 1  [#permalink]

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New post 14 Sep 2018, 11:35
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\(1X + 3X + 5X = 72\)
\(9X = 72\)
\(= 8\)

Answer: E
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Re: If a certain concrete mixture contains gravel, water, and sand in a 1  [#permalink]

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New post 19 Sep 2018, 19:39
AkshdeepS wrote:
If a certain concrete mixture contains gravel, water, and sand in a 1 to 3 to 5 ratio by weight, how many pounds of gravel would be needed to produce 72 pounds of the mixture?

1. 72

2. 40

3. 24

4. 9

5. 8


Trivial application of the k technique:

\(G:W:S = 1:3:5\,\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
? = G = k \hfill \cr
W = 3k \hfill \cr
S = 5k \hfill \cr} \right.\,\,\,\,\,\,\left( {k > 0} \right)\)

\(72 = 9k\,\,\,\, \Rightarrow \,\,\,\,? = k = {{72} \over 9} = 8\,\,\,\,\,\left[ {{\rm{pounds}}} \right]\)


This solution follows the notations and rationale taught in the GMATH method.

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fskilnik.
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Re: If a certain concrete mixture contains gravel, water, and sand in a 1  [#permalink]

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New post 21 Jan 2019, 19:01
AkshdeepS wrote:
If a certain concrete mixture contains gravel, water, and sand in a 1 to 3 to 5 ratio by weight, how many pounds of gravel would be needed to produce 72 pounds of the mixture?

1. 72

2. 40

3. 24

4. 9

5. 8


We can create the ratio:

Gravel : water : sand = x : 3x : 5x

We can create the equation:

x + 3x + 5x = 72

9x = 72

x = 8

So the number of pounds of gravel is 8.

Answer: E
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Re: If a certain concrete mixture contains gravel, water, and sand in a 1   [#permalink] 21 Jan 2019, 19:01
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