The ratio of north american butterflies to south american butterflies at a butterfly park is 5: 3. the ratio of south america butterflies to europe butterflies is 3: 2. there are 30 north american butterflies at the butterfly park

I am not sure exctly what the question is here but if you are wondering how many butterflies tatal for all species here it is:

North American Butterfrlies: 30

South American Butterflies: 18

Europe Butterflies: 12

Step-by-step explanation: To get the total number of butterflies per species you need to mulitply to find the correct ratio given the total number of North American Butterflies is 30

North American Butterflies to South American Butterflies is 5 to 3 so 30/5=6, you then multiply 3*6 to get 18 South American Butterflies.

Then since we now know there are 18 South American Butterflies and the ratio of those to Europe Butterflies are 3 to 2 we take 18/3=6, then multiply 2*6 to get 12 Europe Butterflies.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4