Question

An animal shelter spends $4.00 per day to care for each cat and $5.50 per day to care for each dog. Ashley noticed that the shelter spent $156.50 caring for cats and dogs on Monday. Ashley found a record showing that there were a total of 32 cats and dogs on Monday. How many cats were at the shelter on Monday?

Answer 1

Answer:

There were 13 cats and 19 dogs in the shelter on Monday.

Step-by-step explanation:

Let the number of cats be x.

Let the number of dogs be y.

Given:

Total Number of cats and dogs on Monday = 32

Now Total number of  cats and dogs are equal to sum of number of cats and number of dogs.

Hence Framing in the equation form we get;

$x+y=32\ \ \ \ equation\ 1$

Also Given:

Cost to care each cat per day = $4.00

Cost to care each dog per day = $5.50

Total Money Spent on Monday = $156.50

But Total Money spent depends upon the sum of Cost to care each cat per day multiplied with number of Cats and Cost to care each dog per day multiplied with number of dogs.

Hence equation can be framed as;

$4x+5.5y=156.50 \ \ \ \ equation\ 2$

Now Multiplying equation 1 by 4 we get;

$4(x+y)=32\times4\\4x+4y=128 \ \ \ \ equation\ 3$

Now Subtracting equation 3 from equation 2 we get;

$(4x+5.5y)-(4x+4y)=156.5-128\\\\4x+5.5y-4x-4y= 28.5\\\\1.5y=28.5\\\\y=\frac{28.5}{1.5} = 19$

Now Substituting the value of y in equation 1 we get

$x+y=32\\x+19=32\\x=32-19\\x= 13$

Hence There were 13 cats and 19 dogs in the shelter on Monday.