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In a national park, there are only Hippopotamus or Peacocks. When the

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In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

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New post 17 Apr 2020, 02:27
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In a national park, there are only Hippopotamus or Peacocks. When the heads are counted, it comes out to be 96 and when the legs are counted it comes out to be 336. What is the number of peacocks in the park?

A. 24
B. 48
C. 60
D. 72
E. 80


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Re: In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

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New post 17 Apr 2020, 02:53
1
Let's note h the number of hippos and p the number of peacocks.

Each animal has only one head (assuming there is no genetic engineering going on!) so the number of heads give us the following equation:
(1) h + p = 96

A hippo has 4 legs and a peacock has 2 legs. Therefor, the "leg count" gives us:
(2) 4h+2p = 336 that can also be simplified to 2h+p = 168 (by dividing both sides by 2)

Subtracting equation (1) from equation (2) give us:
2h+p - (h + p) = 168-96

which is equivalent to:
h = 72

The easy mistake here is to go and click (D) straight away !!!!! , but let's remember that we're looking for the number of peacocks rather than hippos!
Using (1) we have p = 96 - h = 96 - 72 = 24

The answer is (B) 24 peacocks
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Re: In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

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New post 17 Apr 2020, 03:21
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Bunuel wrote:
In a national park, there are only Hippopotamus or Peacocks. When the heads are counted, it comes out to be 96 and when the legs are counted it comes out to be 336. What is the number of peacocks in the park?

A. 24
B. 48
C. 60
D. 72
E. 80


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Solution:


Each peacock will have one head and two legs, and each Hippopotamus will have one head and four legs.
Let x and y be the number of peacock and hippopotamus respectively.
    • Heads of peacock + heads of hippopotamus = total heads
      o \(x + y = 96\) …(i)
    • legs of peacock + legs of hippopotamus = total legs
      o \(2x + 4y = 336\)
         \(x + 2y = 168\)…(ii)
    • Equation (i), can be written as;
      o \(y = 96 – x\)
    • On substituting above value in equation (ii), we get
      o \(x +2(96-x) = 168\)
      o \(x + 192 – 2x = 168\)
      o \(192-168 = x\)
      o \(x = 24\)
Hence, the correct answer is Option A.
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In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

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New post 17 Apr 2020, 17:37
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Bunuel wrote:
In a national park, there are only Hippopotamus or Peacocks. When the heads are counted, it comes out to be 96 and when the legs are counted it comes out to be 336. What is the number of peacocks in the park?

A. 24
B. 48
C. 60
D. 72
E. 80


Project PS Butler


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Let Hippopotamus be \(H \) and Peacock be \(P\) . Each Hippopotamus will have \(1 \) head and \(4 \) legs, and each Peacock will have \(1 \) head and \(2 \) legs.

Total number of heads \(=> \)

\(H + P = 96 ----- (i)\)

\(H = 96 - P ----- (ii)\)

Total number of legs \(=>\)

\(4 H + 2 P = 336 ----- (iii)\)

Substituting value of \(H \) in equation \((iii)\), we get;

\(4 (96-P) + 2 P = 336\)

\(384 - 4P + 2P = 336\)

\(384 - 2P = 336\)

\(2P = 384 - 336 = 48\)

\(P = \frac{48}{2} = 24\)

Total number of Peacocks \(= 24\)

Answer A
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In a national park, there are only Hippopotamus or Peacocks. When the  [#permalink]

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New post 31 May 2020, 06:41

Solution


Given
    • Total count of Heads = 96. Total count of Legs = 336.

To Find
    • Number of peacocks.

Approach and Working Out
The question can be solved using the process skill of ‘translation’. Let’s see how.
(Conceptual knowledge needed = Solving linear equations)
    • Let the numbers of hippopotamus be H and that of Peacocks be P.
      • Translating the first statement as H + P =96. Since both H and P have one head each. Thus the number of heads = number of both hippopotamus and peacocks taken together.
    • Using translation again for second statement: 4H + 2P = 336. Since each hippopotamus has 4 legs and each peacock has 2 legs, thus the number of legs of hippopotamus = 4H and number of legs of peacocks = 2P.
    • Solving the two equations gives us H = 72 and P = 24.

Correct Answer: Option A
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In a national park, there are only Hippopotamus or Peacocks. When the   [#permalink] 31 May 2020, 06:41

In a national park, there are only Hippopotamus or Peacocks. When the

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