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The Fishery Diner at the start of business operations had lobsters and

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The Fishery Diner at the start of business operations had lobsters and [#permalink]

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New post 28 Dec 2017, 21:46
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Question Stats:

63% (00:53) correct 38% (01:06) wrong based on 24 sessions

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The Fishery Diner at the start of business operations had lobsters and fish in a seafood tank in a ratio of 2 to 5. Over the first hour of operations no seafood was sold and lobsters were added to the tank. If after adding the two lobsters the ratio of lobsters to fish in the tank was 1 to 2, which of the following is the number of lobsters in the tank at the start of business operations?

A. 1
B. 2
C. 4
D. 8
E. 10

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Re: The Fishery Diner at the start of business operations had lobsters and [#permalink]

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New post 29 Dec 2017, 05:05
Bunuel wrote:
The Fishery Diner at the start of business operations had lobsters and fish in a seafood tank in a ratio of 2 to 5. Over the first hour of operations no seafood was sold and lobsters were added to the tank. If after adding the two lobsters the ratio of lobsters to fish in the tank was 1 to 2, which of the following is the number of lobsters in the tank at the start of business operations?

A. 1
B. 2
C. 4
D. 8
E. 10


Instead of working with equations, we'll work with the answers.
This is an Alternative approach.

Let's start with the median - C.
If there were 4 lobsters at the start then there were 10 fish (as the ratio is 2:5).
Adding two lobsters changes this to 6:10 with is more than 1:2.
(C) is eliminated.
We have too few fish so we'll need to choose a larger number meaning that (B) and (A) are also eliminated.
(If you don't understand this it's OK - just try (B) and see for yourself)
Let's try (D): If there were 8 lobsters at the start then there were 20 fish.
Adding 2 lobsters gives a ratio of 10:20 = 1:2. Yes!
(D) is our answer.
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Re: The Fishery Diner at the start of business operations had lobsters and [#permalink]

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New post 29 Dec 2017, 18:46
1
L = lobster, F = fish
(L / F) = (2 / 5) Equation 1 This is because lobster to fish ratio is 2 to 5.
(L + 2)/F = (1 / 2) Equation 2 This is because after two additional lobsters are added, the ratio becomes 1 to 2.

Equation 1 becomes 5L = 2F after it is cross-multiplied.
Equation 2 becomes 2L + 4 = F after it is cross-multiplied.

I want to eliminate F because we are trying to find L. So I multiply Equation 2 by 2 so it becomes 4L + 8 = 2F Equation 3

I subtract the Equation 3 from Equation 1 to get the equation, 5L - 4L - 8 = 0.
Simplifying the equation gives me L - 8 = 0.
Hence, L = 8 (Answer D)
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The Fishery Diner at the start of business operations had lobsters and [#permalink]

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New post 29 Dec 2017, 22:04
Bunuel wrote:
The Fishery Diner at the start of business operations had lobsters and fish in a seafood tank in a ratio of 2 to 5. Over the first hour of operations no seafood was sold and lobsters were added to the tank. If after adding the two lobsters the ratio of lobsters to fish in the tank was 1 to 2, which of the following is the number of lobsters in the tank at the start of business operations?

A. 1
B. 2
C. 4
D. 8
E. 10

Original ratio: \(\frac{L}{F}= \frac{2x}{5x}\)

No fish added, two lobsters added, and the new ratio is 1 : 2, i.e., \(\frac{1}{2}\)

\(\frac{2x +2}{5x} = \frac{1}{2}\)

\(2(2x +2) = 5x\)
\(4x + 4 = 5x\)
\(x = 4 =\) the multiplier for the original ratio

How many lobsters at the start?
\(x = 4\)
Lobsters (original ratio)
\(= 2x = (2)(4) = 8\)

Answer D
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Re: The Fishery Diner at the start of business operations had lobsters and [#permalink]

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New post 31 Dec 2017, 10:31
Bunuel wrote:
The Fishery Diner at the start of business operations had lobsters and fish in a seafood tank in a ratio of 2 to 5. Over the first hour of operations no seafood was sold and lobsters were added to the tank. If after adding the two lobsters the ratio of lobsters to fish in the tank was 1 to 2, which of the following is the number of lobsters in the tank at the start of business operations?

A. 1
B. 2
C. 4
D. 8
E. 10


Let the initial number of lobsters and fish be 2x and 5x respectively.

After adding 2 lobsters, the total number of lobster = 2x + 2

The new ratio = 1: 2

2x+2 : 5x = 1: 2

4x + 4 = 5x

x = 4

Thus, the initial number of lobster = 2x = 8.

Correct Answer : Option D
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Re: The Fishery Diner at the start of business operations had lobsters and [#permalink]

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New post 31 Dec 2017, 10:38

Method 2



Though the usual method is the quickest way to solve, an alternate method could be the following.

Initial ratio- 2: 5

Final ratio - 1: 2 or 5/2: 5 = 2.5: 5

Notice that the number of fishes are not changing, so I tried to keep the 5 intact in both the ratios, so that I can now simply focus on the number of lobster.

2 becomes, 2.5 when 2 lobsters are added, so we can say that 0.5 in the ratio is equivalent to 2 lobster in acutal.

We need to find the initial number of lobster(i.e 2 in the ratio), so using unitary method, we can say

0.5 is equivalent to 2 lobsters
1 is equivalent to 4 lobsters
Thus, 2 is equivalent to 8 lobsters.

Such ratio manipulation can be helpful in a lot of sums, so thought of sharing this method. :)


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Re: The Fishery Diner at the start of business operations had lobsters and   [#permalink] 31 Dec 2017, 10:38
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