Question

An animal shelter spends $1.50 per day to care for each bird and $8.50 per day to care for each cat. Alexander noticed that the shelter spent $108.00 caring for birds and cats on Tuesday. Alexander found a record showing that there were a total of 30 birds and cats on Tuesday. How many birds were at the shelter on Tuesday?

Answer 1

Answer:

21 birds.

Step-by-step explanation:

Let B represent the number of birds and C represent the number of cats.

We have been given that an animal shelter spends $1.50 per day to care for each bird, so the amount spent on B birds will be 1.50B.

The animal shelter spends $8.50 per day to care for each cat, so the amount spent on C cats will be 8.50C.

Alexander noticed that the shelter spent $108.00 caring for birds and cats on Tuesday. We can represent this information in an equation as:

$1.50B+8.50C=108...(1)$

Alexander found a record showing that there were a total of 30 birds and cats on Tuesday. We can represent this information in an equation as:

$B+C=30...(2)$

We will use substitution method to solve system of linear equations.

From equation (2) we will get,

$C=30-B$

Substituting this value in equation (1) we will get,

$1.50B+8.50(30-B)=108$

$1.50B+255-8.50B=108$

$255-7B=108$

Let us subtract 255 from both sides of our equation.

$255-255+7C=108-255$

$-7B=-147$

Let us divide both sides of our equation by -7.

$\frac{-7B}{-7}=\frac{-147}{-7}$

$B=21$

Therefore, there were 21 birds at the shelter on Tuesday.