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Gordon purchased a television when his local electronics store had a sale. The television was offered at 30% off its original price of $472. What was the sale price Gordon paid?
- A. $141.60
- B. $225.70
- C. $305.30
- D. $330.40
Correct Answer: D
Rationale: To find the sale price after a 30% discount, you need to subtract 30% of the original price from the original price. 30% of $472 is $141.60. Subtracting this discount from the original price gives $472 - $141.60 = $330.40, which is the sale price Gordon paid. Choice A, $141.60, is incorrect as it represents only the discount amount, not the final sale price. Choices B and C are also incorrect as they do not account for the correct calculations of the discount and final sale price.
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Simplify the following expression: 5 x 3 · 9 x 4
- A. 5/12
- B. 8/13
- C. 20/27
- D. 47/36
Correct Answer: A
Rationale: To simplify the expression 5 x 3 · 9 x 4, first perform the multiplications and divisions from left to right: 5 x 3 = 15 and 9 x 4 = 36. So, the expression becomes 15 · 36. When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. Hence, 15 · 36 = 15/36. To simplify the fraction further, find the greatest common divisor, which is 3. Divide both the numerator and denominator by 3 to get the final result: 15/36 = 5/12. Therefore, the correct answer is A. Choices B, C, and D are incorrect because they do not represent the correct simplification of the given expression.
Simplify the following expression: 4 * (2/3) · 1 * (1/6)
- A. 2
- B. 3 1/3
- C. 4
- D. 4 1/2
Correct Answer: C
Rationale: To simplify the expression, first convert the mixed numbers into fractions: 4 * (2/3) · 1 * (1/6). This becomes 4 * 2/3 · 1 * 1/6. Next, perform the multiplication and division from left to right: 8/3 · 1 * 1/6 = 8/3 * 1 * 6 = 8/3 * 6 = 16. Therefore, the correct answer is 4. Choice A (2) is incorrect as it does not represent the final simplified expression. Choice B (3 1/3) is incorrect as it does not match the result of simplifying the expression. Choice D (4 1/2) is incorrect as it does not match the result of simplifying the expression.
Solve for x: 3(x + 4) = 18
- A. x = 2
- B. x = 4
- C. x = 6
- D. x = 8
Correct Answer: C
Rationale: To solve the equation 3(x + 4) = 18, first distribute the 3 to both terms inside the parentheses: 3x + 12 = 18. Next, isolate the variable x by subtracting 12 from both sides: 3x = 6. Finally, divide by 3 to solve for x, giving x = 6. Choice A, x = 2, is incorrect as the correct solution is x = 6. Choices B (x = 4) and D (x = 8) are also incorrect as they do not satisfy the given equation.
Robert is planning to drive 1,800 miles on a cross-country trip. If his car gets 30 miles per gallon and his tank holds 12 gallons of gas, how many tanks of gas will he need to complete the trip?
- A. 3 tanks
- B. 5 tanks
- C. 30 tanks
- D. 60 tanks
Correct Answer: B
Rationale: To find out how many tanks of gas Robert needs for the 1,800-mile trip, first, we calculate the distance his car can travel on a full tank: 30 miles per gallon 12 gallons = 360 miles per tank. Next, divide the total trip distance by the distance per tank: 1,800 miles · 360 miles per tank = 5 tanks. Therefore, Robert will need 5 tanks of gas to complete the cross-country trip. Choices A, C, and D are incorrect as they do not accurately calculate the number of tanks needed based on the given information.
Tom needs to buy ink cartridges and printer paper. Each ink cartridge costs $30. Each ream of paper costs $5. He has $100 to spend. Which of the following inequalities may be used to find the combinations of ink cartridges and printer paper he may purchase?
- A. 30c + 5p ≤ 100
- B. 30c + 5p = 100
- C. 30c + 5p > 100
- D. 30c + 5p < 100
Correct Answer: A
Rationale: The correct inequality is 30c + 5p ≤ 100. This represents the combinations of ink cartridges (c) and printer paper (p) that Tom may purchase, ensuring the total cost is less than or equal to $100. Choice B is incorrect because the total cost should be less than or equal to $100, not equal to. Choices C and D are also incorrect as they indicate the total cost being greater than $100, which is not the case given Tom's budget limit.