ACT Math: Integrating Essential Skills (Drill 2)

Question 1. Darius deposits $2,400 in a savings account that earns 3.5% simple interest per year. How much interest will he earn after 4 years?

• A) $84
• B) $336 ✓
• C) $2,736
• D) $840

Explanation: Simple interest formula: I = P × r × t = 2,400 × 0.035 × 4 = 2,400 × 0.14 = $336. Choice A results from computing interest for only 1 year without multiplying by t: 2,400 × 0.035 = $84. Choice C results from computing the total account balance (principal + interest) instead of just the interest earned: $2,400 + $336 = $2,736. Choice D results from using r = 3.5 as a whole number instead of a decimal: 2,400 × 3.5 × 0.1 = $840, or from computing 2,400 × 0.035 × 10 years.

Question 2. A swimming pool holds 18,000 gallons of water. A pump can drain water at a rate of 25 gallons per minute. If the pool is currently full, how many hours will it take to completely drain the pool?

• A) 12 ✓
• B) 720
• C) 450
• D) 6

Explanation: Time in minutes = 18,000 ÷ 25 = 720 minutes. Convert to hours: 720 ÷ 60 = 12 hours. Choice B results from correctly computing 720 minutes but forgetting to convert to hours, giving the answer in minutes instead. Choice C results from using an incorrect drain rate of 40 gal/min instead of 25: 18,000 ÷ 40 = 450. Choice D results from dividing 720 by 120 instead of 60: 720 ÷ 120 = 6.

Question 3. A coffee shop blends two types of coffee beans. Type A costs $8 per pound and Type B costs $14 per pound. The shop wants to make a 30-pound blend that costs $10 per pound. How many pounds of Type A should be used?

• A) 10
• B) 15
• C) 20 ✓
• D) 24

Explanation: Let a = pounds of Type A. Then (30 − a) = pounds of Type B. Set up the cost equation: 8a + 14(30 − a) = 10 × 30. 8a + 420 − 14a = 300. −6a = −120. a = 20. The shop needs 20 pounds of Type A. Verify: 20 lb × $8 + 10 lb × $14 = $160 + $140 = $300 = 30 × $10 ✓. Choice A results from setting up the equation incorrectly and solving for Type B pounds instead: 30 − 20 = 10. Choice B results from assuming equal parts of each bean: 30 ÷ 2 = 15. Choice D results from a sign error in the equation: solving −6a = −120 as a = −120/5 = 24.

Question 4. A homeowner wants to tile a rectangular kitchen floor that measures 12 feet by 15 feet. Tiles come in boxes that each cover 18 square feet and cost $42 per box. The homeowner plans to buy 10% extra tiles to account for breakage. What is the total cost of the tiles the homeowner will buy?

• A) $378
• B) $420
• C) $462 ✓
• D) $504

Explanation: Floor area = 12 × 15 = 180 sq ft. With 10% extra: 180 × 1.10 = 198 sq ft needed. Boxes needed = 198 ÷ 18 = 11 boxes (exactly). Total cost = 11 × $42 = $462. Choice A results from forgetting the 10% extra: 180 ÷ 18 = 10 boxes × $42 = $420... that is Choice B. Choice A ($378) results from computing 9 boxes × $42, perhaps from dividing 180 by 20 instead of 18. Choice B results from buying exactly enough boxes for the floor area without the 10% extra: 10 × $42 = $420. Choice D results from rounding up to 12 boxes before applying the cost: 12 × $42 = $504.

Question 5. A laptop originally costs $800. The price is first increased by 15%, then later reduced by 20%. What is the final price of the laptop?

• A) $760
• B) $736 ✓
• C) $800
• D) $720

Explanation: After 15% increase: $800 × 1.15 = $920. After 20% decrease: $920 × 0.80 = $736. The net effect is not simply 15% − 20% = −5%. The 20% reduction is applied to the already-increased price of $920, not the original $800. Choice A results from applying the net percent change to the original price as if the changes were independent: $800 × (1 − 0.05) = $800 × 0.95 = $760. Choice C results from incorrectly concluding the changes cancel out (15% up then 15% down would give the original price, but 20% down does not cancel 15% up). Choice D results from computing $800 × 0.90 = $720, using a net change of −10% rather than applying the changes sequentially.