Question 126681: You are under water and you count 40 legs of animals. You come above water and there are ducks and turtles, but a total of 13 of them. How many ducks are there and how many turtles are there? ---I figured out that there are 6 ducks and 7 turtles becuase 6(2 legs)=12 and 7(4 legs)=28 and 12+28=40, but I need to know how to write that in an algebraic equation to get those answers instead of just doing basic multiplication.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let D represent the number of ducks and T represent the number of turtles.
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The problem tells you that there are 13 animals. This means that if you add the number of
ducks to the number of turtles the sum is 13. In equation form this is:
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D + T = 13
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Each duck has 2 legs, so to get the number of duck legs you multiply the number of ducks by 2
to get 2D. And each turtle has 4 legs, so to get the number of turtle legs you multiply the
number of turtles by 4 to get 4T. If you now add these two amounts together, the problem tells
you that the total is 40. In equation form this is:
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2D + 4T = 40
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You now have the two equations you need to solve for the number of ducks and turtles.
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Return to the first equation and solve it for one variable in terms of the other. For
example, let's solve for D in terms of T by subtracting T from both sides of this equation
to get:
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D = 13 - T
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Then go to the second equation and substitute 13 - T in place of D. This substitution
makes the second equation become:
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2(13 - T) + 4T = 40
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Do the distributed multiplication on the left side by multiplying 2 times each of the
terms inside the parentheses to get:
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26 - 2T + 4T = 40
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Get rid of the 26 on the left side by subtracting 26 from both sides and you have:
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-2T + 4T = 14
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Combine the two terms on the left side and this reduces the equation to:
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2T = 14
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Solve for T by dividing both sides of this equation by 2:
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T = 7
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You now know that there are 7 turtles and since there are 13 animals, the remaining
6 animals must be the ducks.
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Hope this helps you to see where your answer of 6 ducks and 7 turtles came from.
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