The ratio of north american butterflies to south american butterflies is 5: 3. the ratio of south american butterflies to european butterflies is 3: 2. there are 30 north american butterflies at the butterfly park. how many south americans butterflies are there? how many european butterflies are there?

There are 18 South American butterflies and  12 European butterflies.

Step-by-step explanation:

Let be "s" the number of South American butterflies at the butterfly park.

You know that the ratio of North American butterflies to South American butterflies at a butterfly park is 5:3 and the number of North American butterflies at the butterfly park is 30.

Based on this, you can write the folllowing proportion:

Solving for "s", you get:

Let be "e" the number of European butterflies at the butterfly park.

Knowing that the ratio of South American butterflies to European butterflies at the butterfly park is 3:2, and knowing that there are 18 South American butterflies, you can write the following proportion:

Solving for "e", you get:

(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

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!