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

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

by BTGModeratorVI » Wed Oct 07, 2020 7:20 am

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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

Source: Magoosh

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### Re: When 12 marbles are added to a rectangular aquarium, the water

by [email protected] » Sat Oct 10, 2020 7:15 am
BTGModeratorVI wrote:
Wed Oct 07, 2020 7:20 am
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

Source: Magoosh
We can solve this question using equivalent ratios

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

Cheers,
Brent

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### Re: When 12 marbles are added to a rectangular aquarium, the water

by [email protected] » Sat Oct 17, 2020 7:59 am
BTGModeratorVI wrote:
Wed Oct 07, 2020 7:20 am
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

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 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.