The ratio of Monarch butterflies to swallowtail in the butterfly garden is 5:3. The ratio of swallowtail to Viceroy is 3:2. There are 30 Monarchs in the park. How many swallowtails are there? Viceroy?

Accepted Solution

There are 18 swallowtails and 12 viceroy in the butterfly garden. Step-by-step explanation:Ratio of monarch to swallowtail = 5:3Ratio of swallowtail to viceroy = 3:2Total monarchs = 30let x be the number of swallowtails.Using proportion; Ratio of monarch to swallowtail :: ratio of no. of monarchs to swallowtails[tex]5:3::30:x[/tex]Product of extreme = Product of mean[tex]5*x=30*3\\5x=90[/tex]Dividing both sides by 5[tex]\frac{5x}{5}=\frac{90}{5}\\x=18[/tex]There are 18 swallowtails in the butterfly garden.Ratio of swallowtail to viceroy = 3:2let y be the number of viceroy.Using proportions;Ratio of swallowtail to viceroy :: Ratio of no. of swallowtail to viceroy[tex]3:2::18:y\\[/tex]Product of extreme = Product of mean[tex]3*y=18*2\\3y=36\\[/tex]Dividing both sides by 3[tex]\frac{3y}{3}=\frac{36}{3}\\y=12[/tex]There are 12 viceroy in the butterfly garden. There are 18 swallowtails and 12 viceroy in the butterfly garden. Keywords: ratio, proportionLearn more about ratios at:brainly.com/question/12896802brainly.com/question/13063819#LearnwithBrainly