While driving through the countryside one day I saw a farmer tending his pigs and ducks in his yard. I was curious to know how many of each he had. I stopped the car and inquired.Leaning on the stile jovially, he replied, 'I have altogether 60 eyes and 86 feet between them.'I drove off trying to calculate in my mind the exact number of ducks and pigs he had. What do you think is the answer?A. 17,13B. 13,17C. 15 ,15D. 10,20
Question
While driving through the countryside one day I saw a farmer tending his pigs and ducks in his yard. I was curious to know how many of each he had. I stopped the car and inquired.Leaning on the stile jovially, he replied, 'I have altogether 60 eyes and 86 feet between them.'I drove off trying to calculate in my mind the exact number of ducks and pigs he had. What do you think is the answer?A. 17,13B. 13,17C. 15 ,15D. 10,20
Solution
To solve this problem, we need to set up a system of equations based on the information given.
Let's denote the number of pigs as P and the number of ducks as D.
From the information given, we know that each animal has 2 eyes. So, the total number of eyes gives us the equation: 2P + 2D = 60.
Simplify this equation, we get: P + D = 30.
We also know that each pig has 4 feet and each duck has 2 feet. So, the total number of feet gives us the equation: 4P + 2D = 86.
Simplify this equation, we get: 2P + D = 43.
Now we have a system of two equations:
- P + D = 30
- 2P + D = 43
Subtract the first equation from the second, we get: P = 13.
Substitute P = 13 into the first equation, we get: D = 30 - 13 = 17.
So, the farmer has 13 pigs and 17 ducks. The answer is B. 13,17.
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