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When 12 marbles are added to a rectangular aquarium, the water in the

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Math Expert
Joined: 02 Sep 2009
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When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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20 Mar 2015, 06:18
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When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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20 Mar 2015, 07:38
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We know that it takes 12 marbles to gain 1.5 inches. Now we need to find out how many marbles we need to gain 2.75 inches.

$$\frac{12 marbles}{1.5 inches} = \frac{x marbles}{2.75 inches}$$

$$x = \frac{12 * 2.75}{1.5} = \frac{12*\frac{11}{4}}{\frac{3}{2}} = \frac{3*11}{\frac{3}{2}} = \frac{33*2}{3} = 11*2 = 22.$$

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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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20 Mar 2015, 08:08
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Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

apart from mathematical equation, the other way is by elimination and estimation...

12marbles-----1 1/2 in...... 24 marbles----3 in

12=4*3marbles-----1 1/2 in=1/2*3
4 marbles----1/2 in...
4*5 marbles----1/2*5=2 1/2..
so ans more than 20 and less than 24...

so ans 22 D..
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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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20 Mar 2015, 11:10
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D

unitary method
3/2 inch is raised by 12 marbles

so 11/4 inch is raised by 12*(2/3)*(11/4)=22
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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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20 Mar 2015, 19:41
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

use the ratio method
(12)/(3/2) = x/(11/4)
x=22

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When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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20 Mar 2015, 22:10
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

easy question for a kudo
As the aquarium is rectangular , the rise per marble will be same at each point.
so ,
$$\frac{12 * 2}{3} = \frac{4*X}{11}$$
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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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23 Mar 2015, 04:27
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

Aqua_Marbles.png [ 20.21 KiB | Viewed 2892 times ]

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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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25 Mar 2015, 02:28
Answer = D = 22

Marbles required $$= \frac{11}{4} * 12 * \frac{2}{3} = 22$$
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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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01 Apr 2015, 06:12
12 marbles = 1 1/2, 1 1/2 = 3/2

Raise to; 2 3/4 = 11 / 4

3/2 = 6/4

You need to go from 6 / 4 to 11 / 4, which is 5 / 4.

12 marbles = 6 / 4
2 marbles = 1 / 4

you need 5 / 4, 5*marbles is 10 marbles.

10 + 12 marbles = 22 marbles.
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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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26 Jan 2019, 12:33
Hi All,

We're told that when 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. We're asked how many marbles must be added to the aquarium in total to raise the water 2 3/4 inches. This question is ultimately about ratios, so you can approach the math in a variety of different ways.

To start, I'm going to convert the mixed fractions into decimals:
12 marbles --> raises the water 1.5 inches
X marbles --> raises the water 2.75 inches

2.75 - 1.5 = 1.25 additional inches needed to be raised

We know that 12 marbles raises the water 1.5 inches, so we can set up a ratio to determine how many marbles would be needed to raise the water an additional 1.25 inches...

1.5/12 = 1.25/X
1.5X = 15
X = 15/1.5 = 10 additional marbles needed.

Thus, we need 12+10 = 22 total marbles.

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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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27 Jan 2019, 05:34
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

$${\rm{aqua}}\,\,{\rm{dimensions}}\,\,{\rm{:}}\,\,a,b,h\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{Volume}}\left( {{\rm{aqua}}} \right) = abh$$

$$M = {\rm{Volume}}\left( {{\rm{marble}}} \right)$$

$$? = x\,\,\,\,\left( {\# \,\,{\rm{marbles}}} \right)$$

$$\left\{ \matrix{ abh\,\,{\rm{ + }}\,\,{\rm{12}} \cdot M = \underbrace {ab}_{{\rm{i}}{{\rm{n}}^2}}\,\, \cdot \,\,\underbrace {\,\left( {{\rm{h}} + 1{1 \over 2}} \right)}_{{\rm{in}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,12M = {3 \over 2}abh \hfill \cr abh\,\,{\rm{ + }}\,\,x \cdot M = \underbrace {ab}_{{\rm{i}}{{\rm{n}}^2}}\,\, \cdot \,\,\underbrace {\,\left( {{\rm{h}} + 2{3 \over 4}} \right)}_{{\rm{in}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,xM = {{11} \over 4}abh \hfill \cr} \right.$$

$$xM = \left[ {{{11} \over 4}abh} \right] = {{11} \over 4}\left( {{2 \over 3} \cdot 12M} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 22$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: When 12 marbles are added to a rectangular aquarium, the water in the  [#permalink]

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30 Jan 2019, 18:13
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

We can create the proportion:

12/(3/2) = x/(11/4)

24/3 = 4x/11

24(11) = 12x

2(11) = x

22 = x

Alternate Solution:

We observe that the addition of each marble raises the water (1 1/2)/12 = (3/2)/12 = 1/8 inches. Thus, to raise the water 2 3/4 = 11/4 inches, we need (11/4)/(1/8) = (11/4) x (8/1) = 11 x 2 = 22 marbles.

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Re: When 12 marbles are added to a rectangular aquarium, the water in the   [#permalink] 30 Jan 2019, 18:13
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