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?
~~~~~~~~~~~~~~


<pre>
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 = {{{20/4}}} = 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.


<U>Answer</U>.  4 goldfish, 5 birds and 7 rabbits.
</pre>


Lessons to learn from this solution:


&nbsp;&nbsp;&nbsp;&nbsp;- Chose the unknowns by a rational way;
&nbsp;&nbsp;&nbsp;&nbsp;- write the system;
&nbsp;&nbsp;&nbsp;&nbsp;- solve the system (I used the substitution method).