Question 105623: Tourist: "How many birds and lions do you have in your zoo?" Zookeeper:"There are 30 heads and 100 feet." Find the number of each animal. I need to know how to set this problem up in a system of linear equations. Thank you.
Answer by fmo(8)   (Show Source):
You can put this solution on YOUR website! Hi,
Birds and lions both only have 1 head each, so that first bit of information tells us how many birds and lions there are. If we represent birds with an x and lions with a y then we can say:
x + y = 30 (eq1)
Birds have 2 feet and lions have 4, so for total feet we'd have to take the number of birds multiplied by the number of feet they have (2) and add that to the number of lions multiplied by their 4 feet, or:
2x + 4y = 100 (eq2)
Those are the two equations that start you off. Next we can take out the common factor of 2 from eq2 and we get:
x + 2y = 50 (eq2/2)
Now subtract eq1 from eq2/2:
x + 2y = 50
x + y = 30
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0x + y = 20
So we know that there are 20 lions. Plug that 20 in place of y in eq1 and we have:
x + 20 = 30
And solving that we find that we have:
x = 10
or 10 birds.
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