AIR MATH

Math Question

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 36 hours each week making carvings. His materials cost him \( \$ 4 \) for each type \( X \) carving and \( \$ 5 \) for each type \( Y \) carving, and he must keep his weekly cost for materials to \( \$ 100 \) or less. If \( x \) is the number of type \( X \) carvings he makes in a week and \( y \) is the number of type \( Y \) carvings he makes in a week, which of the following systems of inequalities models this situation? A. \( 3 x+2 y \geq 36,4 x+5 y \geq 100 \) B. \( 3 x+2 y \leq 36,4 x+5 y \geq 100 \) C. \( 3 x+2 y \leq 36,4 x+5 y \leq 100 \) D. \( 3 x+2 y \geq 36,4 x+5 y \leq 100 \)

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