A woodworking artist makes two types of carvings: type X and type Y. Hespends 3 hours making each type X carving and 2 hours making each type Y carving, and he can spend up to 30 hours each week making carvings. Hismaterials cost him $5 for each type X carving and $7 for each type Y carving,and he must keep his weekly cost for materials to $105 or less. If xis thenumber of type X carvings he makes in a week and yis the number of type Ycarvings he makes in a week, which of the following systems of inequalitiesmodels this situation?

Answer:part C. 3x + 2y < 30, 5x + 7y < 105Step-by-step explanation:Part 1: spends 3 hours making each type X (3x)-each type x will take 3 hours so as the number of type x increases, the hours will increase by 3.spends 2 hours making each type Y (2y)-each type y will take 2 hours so as the number of type y increases, the hours will increase by 2.Part 2: he can spend up to 30 hours each week making carvings. (<30)-because he cannot spend more than 30 hoursTherefore, He has to spend 30 hours or less to make type X and type Y.3x + 2y < 30Part 3: His  materials cost him $5 for each type X carving. (5x)-each type x will take $5 so as the number of type x increases, the cost will increase by 5.His materials cost him $7 for each type Y carving, (7y)-each type y will take $7 so as the number of type y increases, the cost will increase by 7.Part 4: he must keep his weekly cost for materials to $105 or less (<105)-total cost cannot be more than $105.Therefore, the total cost of making x and y should be $105 or less.5x + 7y < 105!!