Awoodworking artist makes two types of carvings: type x and type y. he
spends 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. his
materials 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 the
number of type x carvings he makes in a week and yis the number of type y
carvings he makes in a week, which of the following systems of inequalities
models this situation?

part C. 3x + 2y < 30, 5x + 7y < 105

Step-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 hours

Therefore, He has to spend 30 hours or less to make type X and type Y.

3x + 2y < 30

Part 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

!!

300pi

step-by-step explanation: