Correct Answer: D

Rationale: To calculate Matt's new wage after a 3/20 increase, we need to add this percentage increase to his original wage. The increase in decimal form is 3/20 = 0.15. Therefore, the new wage is w + w(0.15) = w(1 + 0.15) = 1.15w. This means the correct answer is D. Choices A, B, and C are incorrect because they do not account for the full 3/20 increase in the wage. Choice A (0.15w) represents only the increase percentage, not the total new wage. Choice B (0.85w) and Choice C (1.12w) do not accurately calculate the new wage after the increase, leading to incorrect representations of the final wage.

Correct Answer: D

Rationale: To solve the equation 8x − 6 = 3x + 24, start by adding 6 to both sides: 8x − 6 + 6 = 3x + 24 + 6, which simplifies to 8x = 3x + 30. Next, subtract 3x from both sides to get 5x = 30. Finally, divide both sides by 5 to solve for x: x = 6. Therefore, the correct solution is x = 6. Choices A, B, and C are incorrect because they do not result from the correct algebraic manipulation of the equation.

Correct Answer: B

Rationale: To find the amount of paint needed for the four walls of the shed, calculate the total area of the four walls. The shed has two pairs of identical walls. The area of one pair of walls is 5 feet (width) x 7 feet (height) + 4 feet (depth) x 7 feet (height) = 35 ft² + 28 ft² = 63 ft². Since there are two pairs of walls, the total area for the four walls is 2 x 63 ft² = 126 ft². Therefore, Adam will need 126 ft² of paint for the four walls. Choice A, 80 ft², is incorrect as it does not account for the total surface area of all four walls. Choice C, 140 ft², is incorrect as it overestimates the area required. Choice D, 560 ft², is incorrect as it significantly overestimates the amount of paint needed for the shed.

Correct Answer: D

Rationale: To simplify the expression, first multiply 6.4 by 2.8 to get 17.92. Then, divide the result by 0.4 to find the final answer. Therefore, (6.4)(2.8) · 0.4 equals 44.8. Choices A, B, and C are incorrect because they do not represent the correct result of the given expression.

Correct Answer: C

Rationale: To calculate the total cost, convert all weights to kilograms. 800 grams = 0.8 kilograms; 300 grams = 0.3 kilograms. Add up the weights: 1.2 kg + 0.8 kg + 0.3 kg = 2.3 kg. Multiply the total weight by the cost per kilogram: 2.3 kg $4/kg = $9.20. Therefore, the total cost of her produce is $9.20. Choice A, $4.40, is incorrect as it does not account for the total weight of all the fruits. Choice B, $5.24, is incorrect as it does not accurately calculate the total cost based on the given weights and price per kilogram. Choice D, $48.80, is incorrect as it is significantly higher than the correct total cost and suggests an incorrect calculation method.