A woodworking 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?

Question

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Respuesta :

absor201 absor201 · Answer 1 · 2019-06-27T21:34:23+02:00

Answer:

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

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