Question 1074575: Holly is selling, goldfish, birds, and rabbits. Goldfish are $1, birds are $5, and rabbits are $10. She has 16 animals in total. If she sells all of them she will earn $99. The number of goldfish plus the number of birds is 2 more than the number of rabbits. How many of each animal does she have?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52810)   (Show Source):
You can put this solution on YOUR website! .
Holly is selling, goldfish, birds, and rabbits. Goldfish are $1, birds are $5, and rabbits are $10. She has 16 animals in total.
If she sells all of them she will earn $99.
The number of goldfish plus the number of birds is 2 more than the number of rabbits.
How many of each animal does she have?
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Let G be the number of goldfish and B be the number of birds.
Then the number of rabbits is G + B -2.
Thus we have these equations:
G + B + (G+B-2) = 16 (1) (the number of animals in total)
G + 5B + 10*(G+B-2) = 99 (2) (dollars; the total cost)
You have 2 equations for 2 unknowns. Simplify and write is the standard form:
2G + 2B = 18 (1')
11G + 15B = 119 (2')
Or even simpler
G + B = 9 (1'')
11G + 15B = 119 (2'')
Now express G = 9-B from (1'') and substitute it into (2''). You will get
11(9-B) + 15B = 119, or
99 - 11B + 15B = 119, or
4B = 119-99 = 20, ---> B =  = 5.
Thus there are 5 birds.
Then the number of goldfish is G = 9 - B = 4,
and the number of rabbits is G + B - 2 = 4 + 5 - 2 = 7.
Answer. 4 goldfish, 5 birds and 7 rabbits.
Lessons to learn from this solution:
- Chose the unknowns by a rational way;
- write the system;
- solve the system (I used the substitution method).
Answer by josgarithmetic(39620)  (Show Source):
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