Question

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?

Answer 1

`C+B = 21` (1)

`1.5 B + 7.5 C =73.50` (2)

`C = 21-B` (3)

`1.5 B +157.5 -7.5 B = 73.50`

`157.5 -73.5 = 7.5B -1.5 B= 6B`

`B = 14`

An solving for C from (3) we got:

`C = 21-14 = 7`

So then on wednesday are 7 cats and 14 birds

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:

`C+B = 21` (1)

`1.5 B + 7.5 C =73.50` (2)

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

`C = 21-B` (3)

Replacing (3) into (2) we got:

`1.5B+7.5(21-B)= 73.50`

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

`1.5 B +157.5 -7.5 B = 73.50`

`157.5 -73.5 = 7.5B -1.5 B= 6B`

`B = 14`

An solving for C from (3) we got:

`C = 21-14 = 7`

So then on wednesday are 7 cats and 14 birds