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There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
- a)20
- b)30
- c)50
- d)60
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
There are deer and peacocks in a zoo. By counting heads they are 80. T...
**Problem Solving:**
To solve this problem, we can use a system of linear equations. Let's assume that the number of deer is represented by 'x' and the number of peacocks is represented by 'y'.
**Step 1: Formulate the Equations:**
We are given two pieces of information:
1. The total number of heads is 80.
2. The total number of legs is 200.
From these two pieces of information, we can form two equations:
Equation 1: x + y = 80 (since the total number of heads is 80)
Equation 2: 4x + 2y = 200 (since each deer has 4 legs and each peacock has 2 legs)
**Step 2: Solve the Equations:**
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's solve it using the method of substitution.
From Equation 1, we can express x in terms of y: x = 80 - y
Substituting this value of x into Equation 2, we get:
4(80 - y) + 2y = 200
Simplifying the equation, we have:
320 - 4y + 2y = 200
Combining like terms, we get:
-2y = 200 - 320
-2y = -120
Dividing both sides by -2, we get:
y = 60
**Step 3: Find the Number of Peacocks:**
From our solution, we found that y = 60, which represents the number of peacocks.
Therefore, the correct answer is option D) 60.
To solve this problem, we can use a system of linear equations. Let's assume that the number of deer is represented by 'x' and the number of peacocks is represented by 'y'.
**Step 1: Formulate the Equations:**
We are given two pieces of information:
1. The total number of heads is 80.
2. The total number of legs is 200.
From these two pieces of information, we can form two equations:
Equation 1: x + y = 80 (since the total number of heads is 80)
Equation 2: 4x + 2y = 200 (since each deer has 4 legs and each peacock has 2 legs)
**Step 2: Solve the Equations:**
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's solve it using the method of substitution.
From Equation 1, we can express x in terms of y: x = 80 - y
Substituting this value of x into Equation 2, we get:
4(80 - y) + 2y = 200
Simplifying the equation, we have:
320 - 4y + 2y = 200
Combining like terms, we get:
-2y = 200 - 320
-2y = -120
Dividing both sides by -2, we get:
y = 60
**Step 3: Find the Number of Peacocks:**
From our solution, we found that y = 60, which represents the number of peacocks.
Therefore, the correct answer is option D) 60.
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Community Answer
There are deer and peacocks in a zoo. By counting heads they are 80. T...
Let x and y be the number of deer and peacocks in the zoo respectively. Then,
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
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There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?a)20b)30c)50d)60Correct answer is option 'D'. Can you explain this answer?
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