Sharpen your problem-solving skills with this set of medium-level ACT Math word problems focusing on real-life scenarios and practical math applications. Tackle questions designed to help you master key concepts like ratios, percentages, distance, and more, crucial for success on the ACT exam.
A train travels at a constant speed of 60 miles per hour. How far will it travel in 2.5 hours?
Explanation: Multiplying the speed (60 miles per hour) by the time (2.5 hours) gives 150 miles. Option A, 120 miles, results from incorrectly multiplying by 2 hours instead of 2.5. Option C, 90 miles, uses a speed of 36 miles per hour, which doesn't match the scenario. Option D, 100 miles, may result from multiplying 50 miles per hour by 2. The correct answer efficiently applies the distance formula: distance equals rate times time.
Sarah buys a jacket that originally costs $80 but is on sale for 25% off. What is the sale price of the jacket?
Explanation: A 25% discount on $80 is $20 (25% of 80), so subtracting that from the original price gives $60. Option B, $65, might result from taking off only 18.75%, which is incorrect. Option C, $55, comes from subtracting 31.25% off the original price, and option D, $70, might result from a 12.5% discount. Only $60 properly reflects a 25% reduction from $80.
In a recipe, the ratio of flour to sugar is 3:2. If you use 6 cups of flour, how many cups of sugar should you use to keep the same ratio?
Explanation: The ratio 3:2 means for every 3 parts flour, there are 2 parts sugar. With 6 cups of flour (which is double 3), you need twice the sugar: 2 × 2 = 4 cups. Option A, 5 cups, exceeds the proper ratio. Option B, 2 cups, keeps the original amount of sugar, not accounting for doubling. Option D, 3 cups, matches the flour, not the 3:2 ratio. Four cups accurately maintains the original proportion.
If the average of five test scores is 84, what is the sum of the five test scores?
Explanation: The average is the sum divided by the number of scores, so 84 × 5 = 420. Option B, 400, comes from multiplying 80 by 5, which uses the wrong average. Option C, 405, results from using 81 instead of 84. Option D, 425, uses 85 as the average. 420 is the only answer consistent with an average of 84 over five scores.
If twice a number, increased by 9, equals 23, what is the number?
Explanation: Let x be the number: 2x + 9 = 23, so 2x = 14, and x = 7. Option A, 8, comes from subtracting 9 instead of adding. Option B, 6, may result from dividing incorrectly. Option D, 5, is chosen if you subtract 9 and then misapply the division step. Only 7 solves the equation based on the scenario described.