Question

The total number of animals in a shelter is modeled by f(x) = 2x2 - 45x, where x represents the number of

cages at the facility. How many cages are at the facility if it has a total of 243 animals there?
A. 25
B. 27
C. 33
D. 39

Answer 1

B. 27 is the answer.

Explanation:

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Answer 2

B: 27

Explanation:

The total number of animals in a shelter is modeled by the function:

`f(x)=2x^2-45x`

Where x is the number of cages at the facility.

We want to determine the number of cages if there are a total of 243 animals at the shelter.

So, we can set our function to 243 and solve for x:

`243=2x^2-45x`

Subtract 243 from both sides:

`2x^2-45x-243=0`

Solve the quadratic. Factoring and completing the square seems too difficult, so we can use the quadratic formula:

`\displaystyle x=(-b\pm√(b^2-4ac))/(2a)`

In this case, a = 2, b = -45, and c = -243. Substitute:

`\displaystyle x=(-(-45)\pm√((-45)^2-4(2)(-243)))/(2(2))`

Evaluae:

`\displaystyle x=(45\pm√(3969))/(4)`

Evaluate:

`\displaystyle x=(45\pm63)/(4)`

Therefore, our two solutions are:

`\displaystyle x=(45+63)/(4)=27\text{ or } x=(45-63)/(4)=-(9)/(2)`

Since we cannot have negative or half a cage, we can ignore the second solution.

Therefore, there are a total of 27 cages at the shelter.

Our answer is B.