The total cost (in dollars) of ordering graduation announcements is represented by the piecewise function (photo of function) a. determine the cost of ordering 25 announcements. then determine the cost of ordering 24 announcements. b. for what number of announcements less than 25 is it financially better to purchase 25 announcements?

Part (a) :  The cost of ordering 25 announcements.

we need to substitute with x=25 in the middle function which is {1.25x+15}

so, the cost of ordering 25 announcements = 1.25 * 25 + 15 = $46.25

Part (b) :  The cost of ordering 24 announcements.

we need to substitute with x=24 in the upper function which is {1.5x+15}

so, the cost of ordering 24 announcements = 1.5 * 24 + 15 = $51

Part (c): what number of announcements less than 25 is it financially better to purchase 25 announcements?

We need to find x which will give c(x) is greater than $46.25 and less than or equal $51

By graphing the function and making the the boarders of c(x) at $46.25 and $51

The intersection with the function {1.25x+15} will give us the value of x which is 21 and 24

So, The number of announcements less than 25 is financially better to purchase 25 announcements:   21 ≤ x < 25

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3