Question

An animal shelter spends $4.50 per day to care for each bird and $5.50 per day to care for each cat. Nathaniel noticed that the shelter spent $142.50 caring for birds and cats on Thursday. Nathaniel found a record showing that there were a total of 27 birds and cats on Thursday. How many birds were at the shelter on Thursday?

Answer 1

The number of birds are 6 and number of cats are 21 at the shelter on Thursday .

Explanation:

Let us assume that the number of bird be x .

Let us assume that the num ber of cat be y .

As given

An animal shelter spends $4.50 per day to care for each bird and $5.50 per day to care for each cat. Nathaniel noticed that the shelter spent $142.50 caring for birds and cats on Thursday.

4.50x + 5.50y = 142.50

Simplify the above

`(450x)/(100) + (550y)/(100) = (14250)/(100)`

450x + 550y = 14250

As given

Nathaniel found a record showing that there were a total of 27 birds and cats on Thursday.

x + y = 27

Two equations are

450x + 550y = 14250

x + y = 27

Multiply x + y = 27 by 450 and subtracted from 450x + 550y = 14250 .

450x - 450x + 550y - 450y = 14250 - 12150

100y = 2100

`y = (2100)/(100)`

y = 21

Putting the value of y in the equation x + y = 27 .

x + 21 = 27

x = 27 - 21

x = 6

Therefore the number of birds are 6 and number of cats are 21 at the shelter on Thursday .