John and his son are building a boxcar for a group competition. According to the rules of the competition, the length of the car must be 3 inches greater than its width. Also, the width of the car must be at least 2 inches greater than the radii of the wheels. When they signed up for the competition, they were given a kit containing everything they needed to build the car except for the base and the wheels. According to the rules of the competition, they must spend no more than $50. The cost of the base will be $0.50 per square inch and the cost of each of the 4 wheels will be $2.25 per inch of radius. If x represents the width of the car and y represents the radii of the wheels, then which of the following systems of inequalities can be used to determine the length and width of the car and the radii of the wheels?

Question

Mathematics

Rocco Frost

9 November, 04:58

John and his son are building a boxcar for a group competition. According to the rules of the competition, the length of the car must be 3 inches greater than its width. Also, the width of the car must be at least 2 inches greater than the radii of the wheels. When they signed up for the competition, they were given a kit containing everything they needed to build the car except for the base and the wheels. According to the rules of the competition, they must spend no more than $50. The cost of the base will be $0.50 per square inch and the cost of each of the 4 wheels will be $2.25 per inch of radius. If x represents the width of the car and y represents the radii of the wheels, then which of the following systems of inequalities can be used to determine the length and width of the car and the radii of the wheels?

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Answers (1)

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Kinsley Golden · Answer 1

x ≥ y + 2

0.50 (x) (x+3) + 2.25 (4) (y) ≤ 50

Step-by-step explanation:

x = width of the car

x+3 = length of the car

y = radius of the car

The width must be at least 2 inches greater than the radius, so:

x ≥ y + 2

The total cost must be no more than $50, so:

0.50 (x) (x+3) + 2.25 (4) (y) ≤ 50