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
Answer: D
Source: Magoosh
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When 12 marbles are added to a rectangular aquarium, the water
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BTGModeratorVI
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We can solve this question using equivalent ratiosBTGModeratorVI wrote: ↑Wed Oct 07, 2020 7:20 amWhen 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
Answer: D
Source: Magoosh
We'll use the ratio: #of marbles/rise (in inches)
Let x = the number of marbles required to raise the water 2 3/4 inches (aka 2.75 inches).
We can write: 12/1.5 = x/2.75
Cross multiply to get: (1.5)(x) = (12)(2.75)
Simplify: 1.5x = 33
Solve: x = 33/1.5 = 22
Answer: D
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Solution:BTGModeratorVI wrote: ↑Wed Oct 07, 2020 7:20 amWhen 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
Answer: D
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 inch. 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.
Answer: D
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