Each of the dinners served at a banquet was either chicken or beef or fish. The ratio of the number of chicken dinners to the number of beef dinners to the number of fish dinners served at the banquet was 7:5:2, respectively. If there were more than 5 fish dinners served at the banquet, what was the total number of dinners served at the banquet?

Answer:Total dinners served at the banquet = 42Step-by-step explanation:chicken:beef:fish = 7:5:2Chicken = [tex]\frac{7}{2} Fish[/tex] = [tex]\frac{7}{5} Beef[/tex]Beef = [tex]\frac{5}{2} Fish[/tex] = [tex]\frac{5}{7} Chicken[/tex]Fish = [tex]\frac{2}{7} Chicken[/tex] = [tex]\frac{2}{5} Beef[/tex]Fish > 5...........(i)Beef + Fish < 30[tex]\frac{5}{2} Fish[/tex] + Fish < 30Fish < 8.57........(ii)Beef + [tex]\frac{2}{5} Beef[/tex] < 30Beef < 21.43.........(iii)[tex]\frac{5}{7} Chicken[/tex] + [tex]\frac{2}{7} Chicken[/tex] < 30Chicken < 30.........(iv)Chicken < 25........(v)[tex]\frac{7}{2} Fish[/tex] < 25Fish < 7.143........(vi)[tex]\frac{7}{5} Beef[/tex] < 25Beef < 17.857........(vii)From (i), (ii) and (vi)Fish > 5; Fish < 8.57; Fish <7.143;Therefore: 5 < Fish < 7.143So fish is either 6 or 7From (iii) and (vii)Beef < 21.43; Beef < 17.857;Therefore Beef < 17.857If Fish = 6, Beef = 15;If Fish = 7, Beef = 17.5From (iv) and (v)Chicken < 30; Chicken <25;Therefore Chicken < 25If Fish = 6, Chicken = 21;If Fish = 7, Beef = 24.5Since meals must be whole numbers, Fish = 6, Beef = 15, Chicken = 21Total = chicken + beef + fish = 21 + 15 + 6 = 42