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Question

A zoo is building a new large-cat exhibit. Part of the space will be used for lions and part for leopards. The exhibit will house eight large cats in all. Expenses for lion will be about $8000 per year, and expenses for a leopard will be about$6000 per year. Write an equation that can be used to find y, the yearly expenses for the eight cats in the exhibit when x of the cats are lions.

Solution

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Because $x$ represents the number of lions, then $8-x$ represents the number of leopards. We let $y$ represent the yearly expenses for the eight cats, in dollars.

The total yearly expenses is given by:

$\text{total yearly expense}=\text{yearly expenses for lions}+\text{yearly expenses for leopards}$

Using the variables and the given rates for the cats,

$\color{#c34632}{y=8000x+6000(8-x)}$

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