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?

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:

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:

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

From equation (2) we will get,

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

Let us subtract 255 from both sides of our equation.

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

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

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204