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An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday. Write an equation to represent the possible numbers of cats and dogs that could have been at the shelter on Wednesday. Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat's numbers possible? Use your equation to justify your answer. Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on Wednesday. How many cats were at the shelter on Wednesday?

Respuesta :

Answer:

The equation representing the equation of number of cat and dogs in the shelter is [tex]2.35c+5.5d =89.5[/tex].

So Pat's Number are not possible according to equation.

There were 10 cats in the animal shelter on Wednesday.

Step-by-step explanation:

Given:

Cost spend on each cat per day = $2.35

Cost spend on each Dog per day = $5.50

Total amount spent on Wednesday = $89.50

Now Let the number of cats be 'c'.

Also Let the number of dogs be 'd'.

So we know that;

Total amount spent  is equal to Cost spend on each cat multiplied by number of cats plus Cost spend on each dogs multiplied by number of dogs.

framing in equation form we get;

[tex]2.35c+5.5d =89.5 \ \ \ \ equation \ 1[/tex]

Hence the equation representing the equation of number of cat and dogs in the shelter is [tex]2.35c+5.5d =89.5[/tex]

Now Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat's numbers possible

So we can say 'c' = 8 and 'd' = 14

Substituting the value in above equation we get;

[tex]2.35c+5.5d = 2.35\times 8 +5.5 \times 14 = 18.8 + 77 = 95.8[/tex]

But according to question it must be equal to 89.5, which is not true.

Hence Pat number's are not possible with given equation.

Now Pat found a record showing that there were a total of 22 cats and dogs at the shelter on Wednesday.

Total number of animals in shelter = 22

So we can say that;

Total number of animals in shelter is equal to number of cats plus number of dogs.

[tex]c+d =22 \ \ \ \ equation\ 2[/tex]

Now Multiplying the equation 2 by 2.35 we get;

[tex]2.35(c+d) =22\times 2.35\\\\2.35c+2.35d = 51.7 \ \ \ \ equation \ 3[/tex]

Now Subtracting equation 3 from equation 1 we get;

[tex](2.35c+5.5d)-(2.35c+2.35d)=89.5-51.7\\\\2.35c+5.5d-2.35c-2.35d = 37.8\\\\3.15d =37.8\\\\d =\frac{37.8}{3.15} =12[/tex]

Now substituting the value of 'd' in equation 2 we get;

[tex]c+d =22\\\\c+12=22\\\\c=22-12 =10[/tex]

Hence there were 10 cats in the animal shelter on Wednesday.

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