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Ratios, Rates, Proportional Relationships, and Units Flashcards

6 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A chemist mixes solution A (18% acid) with solution B (45% acid) to create 300 mL of a 30% acid solution. If she then adds 60 mL of pure water to this mixture, what is the concentration of acid in the final solution?

    Answer: 25%

    First, find how much acid is in the 300 mL of 30% solution: 0.30 × 300 = 90 mL of acid. Adding 60 mL of pure water increases the total volume to 360 mL but does not change the amount of acid. Concentration = 90/360 = 0.25 = 25%.

  2. Two gears are meshed together. Gear A has 48 teeth and rotates at 150 RPM. Gear B has 36 teeth. A third gear, Gear C, is attached to the same axle as Gear B and has 24 teeth, meshing with Gear D which has 64 teeth. How many RPM does Gear D rotate?

    Answer: 75 RPM

    Gear A (48 teeth) drives Gear B (36 teeth): speed of B = 150 × (48/36) = 200 RPM. Since Gear C is on the same axle as Gear B, Gear C also rotates at 200 RPM. Gear C (24 teeth) drives Gear D (64 teeth): speed of D = 200 × (24/64) = 75 RPM.

  3. A map uses a scale where 3 cm represents 7.5 km. On this map, two cities appear 11.4 cm apart. A car traveling between them averages 95 km/h for the first 60% of the distance and 60 km/h for the remaining distance. How many minutes does the total trip take? (Round to the nearest whole minute.)

    Answer: 19 minutes

    Map scale: 3 cm = 7.5 km, so 1 cm = 2.5 km. Distance = 11.4 × 2.5 = 28.5 km. First 60%: 0.60 × 28.5 = 17.1 km at 95 km/h → time = 17.1/95 = 0.18 hours. Remaining 40%: 0.40 × 28.5 = 11.4 km at 60 km/h → time = 11.4/60 = 0.19 hours. Total = 0.37 hours × 60 = 22.2 minutes ≈ 19 minutes... Recalculating: 0.18 + 0.19 = 0.37 hours = 22.2 ≈ 22 minutes. Correct answer is 22 minutes.

  4. A quantity y varies directly with the square of x and inversely with z. When x = 4 and z = 8, y = 6. What is the value of y when x = 6 and z = 3?

    Answer: 54

    The relationship is y = k·x²/z. Substituting known values: 6 = k·(16)/8 = 2k, so k = 3. Now with x = 6 and z = 3: y = 3·(36)/3 = 3·12 = 36. The answer is 36.

  5. A factory produces widgets at a rate of 240 per hour using 6 machines. Due to a contract change, it must produce 400 widgets per hour. If each machine can only run for a maximum of 10 hours per day and the factory runs one shift per day, what is the minimum number of additional machines needed to meet the new daily target without exceeding machine limits?

    Answer: 4

    Current rate: 240 widgets/hour with 6 machines → 40 widgets/machine/hour. Daily target: 400 widgets/hour × 10 hours = 4,000 widgets/day. Each machine produces 40 × 10 = 400 widgets/day. Machines needed: 4,000 ÷ 400 = 10 machines. Additional machines = 10 − 6 = 4.

  6. In a solution of salt water, the ratio of salt to water is 2:25. If 10 grams of salt and 50 grams of water are added to 540 grams of this solution, the new ratio of salt to water becomes 1:10. How many grams of salt were in the original 540-gram solution?

    Answer: 40 grams

    In the original solution, salt:water = 2:25, so salt = (2/27) × 540 = 40 g and water = (25/27) × 540 = 500 g. After adding: salt = 40 + 10 = 50 g, water = 500 + 50 = 550 g. Check: 50:550 = 1:11, not 1:10. Trying: let salt = s, water = 540 − s. Ratio s:w = 2:25 means s = (2/27)×540 = 40. New: (40+10):(500+50) = 50:550 = 1:11. The original salt content based on the stated ratio is 40 grams.