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# Finding which system of equations represents the situtation

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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