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An animal shelter spends $1.50 per day to care for each bird and $7.50 per day to care for each cat. Matthew noticed that the shelter spent $73.50 caring for birds and cats on Wednesday. Matthew found a record showing that there were a total of 21 birds and cats on Wednesday. How many birds were at the shelter on Wednesday?

Respuesta :

Answer:

[tex] C+B = 21[/tex]   (1)

[tex] 1.5 B + 7.5 C =73.50[/tex]  (2)

[tex] C = 21-B[/tex]   (3)

[tex] 1.5 B +157.5 -7.5 B = 73.50[/tex]

[tex] 157.5 -73.5 = 7.5B -1.5 B= 6B[/tex]

[tex] B = 14[/tex]

An solving for C from (3) we got:

[tex] C = 21-14 = 7[/tex]

So then on wednesday are 7 cats and 14 birds

Step-by-step explanation:

We can define the following notation:

C= represent the number of cats on Wednesday

B= represent the number of birds on Wednesday

From the info given we have the following two conditions:

[tex] C+B = 21[/tex]   (1)

[tex] 1.5 B + 7.5 C =73.50[/tex]  (2)

We can solve C from equation (1) and we got:

[tex] C = 21-B[/tex]   (3)

Replacing (3) into (2) we got:

[tex] 1.5B+7.5(21-B)= 73.50[/tex]

And solving for B from the last expression gives to us that:

[tex] 1.5 B +157.5 -7.5 B = 73.50[/tex]

[tex] 157.5 -73.5 = 7.5B -1.5 B= 6B[/tex]

[tex] B = 14[/tex]

An solving for C from (3) we got:

[tex] C = 21-14 = 7[/tex]

So then on wednesday are 7 cats and 14 birds

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