Eighteen people went on a fishing trip and each caught at least one fish. Seventeen people caught a flounder and sixteen caught a bluefish. Using a Venn diagram to represent the people who caught each fish, and the information that no one caught more than one of each fish, the solution is that fifteen people caught both a flounder and a bluefish.
2. P.O.T.W! Eighteen people charted a fishing boat, and each person caught at least one fish. Seventeen people caught a flounder, while 16 caught a bluefish. If only flounder and bluefish were caught and no one caught more than one of each type, how many people caught both a flounder and a bluefish?
3. Solution In the Venn Diagram, F=the set of people who caught flounder and B=the set of people who caught bluefish, with x, y, and z representing subsets of each set. Since everyone caught at least one fish, we know that x+y+z=18. The facts that 17 people caught flounder and 16 people caught bluefish lead to the equations x+y=17 and y+z=16, and these equations imply, respectively, that z=1 and x=2. After accounting for the 3 people who catch only one fish, 15 remain who caught both a flounder and a bluefish. Answer:15 people
