SOLUTION: A hunter returns with 27 heads and 78 feet. If he only brought back ducks and rabbits, how many did he bring back of each? I need help understanding how to write the equation. I

Question 499746: A hunter returns with 27 heads and 78 feet. If he only brought back ducks and rabbits, how many did he bring back of each? I need help understanding how to write the equation. I know H=27, F=78, D=?, R=? and each duck has 2 feet and each rabbit has 4 feet? not sure how to get all this into an equation. i think it will be multiple equations.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The "foot value" of a duck = 2.
The "foot value" of a rabbit = 4.
D = number of duck heads
2D = number of duck feet
R = number of rabbit heads
4R = number of rabbit feet
.
D + R = 27 (given)
2D + 4R = 78 (given)
.
Note that:
D = 27-R
.
Substitute into second equation to find R.
.
2(27-R) +4R = 78
54 -2R + 4R = 78
Collect
54 +2R = 78
Subtract 54 from both sides
2R = 24
Divide both sides by 2
R = 12
.
So,
D = 27-12
D = 15
.
Check the number of feet to be sure this is the answer.
.
15*2 = 30 duck feet
12*4 = 48 rabbit feet
Total = 78 feet.
Correct.
.
Re-read the question to be sure to answer.
Answer:
He brought back 12 rabbits and 15 ducks.
.
Done.
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