Week 15 Review: Understanding Percentages and Inequalities

• 20%

• 25%

• 30%

• 15%

Answer explanation

To find the percent decrease, subtract the new price from the old price: 80 - 60 = 20. Then, divide the decrease by the original price: 20 / 80 = 0.25. Multiply by 100 to get the percentage: 0.25 x 100 = 25%. Thus, the correct answer is 25%.

• 15%

• 20%

• 25%

• 30%

Answer explanation

To find the percent increase, subtract the old value from the new value: 12,000 - 10,000 = 2,000. Then, divide the increase by the original value: 2,000 / 10,000 = 0.2. Multiply by 100 to get the percentage: 0.2 x 100 = 20%. Thus, the correct answer is 20%.

A student estimated that a book weighs 1.5 kg, but the actual weight is 1.8 kg. What is the percent error in the student's estimation?

• 10%

• 15%

• 16.67%

• 20%

Answer explanation

To find the percent error, use the formula: Percent Error = |Estimated - Actual| / Actual x 100. Here, |1.5 - 1.8| / 1.8 x 100 = 0.3 / 1.8 x 100 = 16.67%. Thus, the correct answer is 16.67%.

Answer explanation

To solve the inequality 3x + 5 < 14, subtract 5 from both sides to get 3x < 9. Then, divide by 3 to find x < 3. Thus, the correct answer is x < 3.

• 25%

• 30%

• 35%

• 40%

Answer explanation

To find the percent decrease, subtract the sale price from the original price: 50 - 35 = 15. Then, divide the decrease by the original price: 15 / 50 = 0.30. Multiply by 100 to get 30%. The correct answer is 25%.

If a population of a town increased from 5,000 to 6,500, what is the percent increase?

• 25%

• 30%

• 35%

• 40%

Answer explanation

To find the percent increase, subtract the old population (5000) from the new population (6500), which gives 1500. Then, divide by the old population (5000) and multiply by 100: (1500/5000) * 100 = 30%. Thus, the correct answer is 30%.

Answer explanation

To solve the inequality 5x - 7 ≥ 18, add 7 to both sides: 5x ≥ 25. Then, divide by 5: x ≥ 5. Thus, the correct answer is x ≥ 5.

A student calculated the area of a rectangle to be 48 square meters, but the actual area is 50 square meters. What is the percent error in the student's calculation?

• 2%

• 4%

• 5%

• 6%

Answer explanation

To find the percent error, use the formula: Percent Error = |(Actual - Estimated)| / Actual * 100. Here, |50 - 48| / 50 * 100 = 4%. Thus, the percent error in the student's calculation is 4%.

• 20%

• 25%

• 30%

• 35%

Answer explanation

To find the percent increase, subtract the original price from the new price: 250 - 200 = 50. Then, divide the increase by the original price: 50 / 200 = 0.25. Multiply by 100 to get the percentage: 0.25 x 100 = 25%. Thus, the correct answer is 25%.

Answer explanation

To solve for x in the equation 2x + 3 = 11, subtract 3 from both sides to get 2x = 8. Then, divide both sides by 2 to find x = 4. Thus, the correct answer is x = 4.