Answer:
19
Step-by-step explanation:
We can solve this problem using a system of equation in two unknowns.
Let b = number of birds.
Let c = number of cats.
The care of a bird costs $5.50, so for b number of birds, the cost of care is 5.5b.
The care of a cat costs $8.50, so for c number of cats, the cost of care is 8.5c.
The total cost of care for the birds and cats is 5.5b + 8.5c.
The total cost of care is $291.50. This must equal the expression we have above, so we get our first equation.
5.5b + 8.5c = 291.5
The total number of birds and cats is b + c, but we are told it is 41, so our second equation is:
b + c = 41
We now have the following system of two equations in two unknowns.
5.5b + 8.5c = 291.5
b + c = 41
Rewrite the first equation.
Multiply both sides of the second equation by -8.5, and write it under the first equation. Then add the equations.
5.5b + 8.5c = 291.5
+ -8.5b - 8.5c = -348.50
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-3b = -57
Divide both sides of the equation by -3.
b = 19
Answer: there were 19 birds
