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There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situtaion?

 

A. 4x+2y=15, x+y=44

B. x=2y+44, 4x=y+15

C. 2x-4y=44, x-y=15

D. x-y=15, 4x+2y=44

 Dec 17, 2020
 #1
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x + y = 15     the number of chickens and horses

4x+2y = 44

I would say A   but it appears incorrectly entered as an answer

    or maybe D   if it were   x+y = 15   

 Dec 17, 2020
 #2
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Let x be the number of animals with 4 legs  

and y be the number of animals with 2 legs  

 

 So, 4 legs on x animals  

plus 2 legs on y animals                     expressed as   4x + 2y = 44  

 

total number of animals                      expressed as      x + y = 15   

 

y = 15 – x so sub into 1st equation     4(x) + 2(15 – x) =  44

                                                            4x + 30 – 2x     =  44

                                                                               2x  =  14

                                                                                 x  =  7       animals with 4 legs, i.e., horses 

 

sub 7 for x                                                           7 + y  =  15  

                                                                                  y  =  8       animals with 2 legs, i.e., chickens  

 

Check

7 horses have                28 legs  

8 chickens have             16 legs  

total legs                        44 legs

 Dec 17, 2020

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