Unit Rate Applications

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Unit Rate Applications · Grade 6 · Worksheet 1

1. Olivia buys 15 kilograms of apples for $60. What is the unit price per kilogram? Answer: 4 Solution: Total cost = $60 Total weight = 15 kilograms Unit price = Total cost ÷ Total weight = 60 ÷ 15 60 ÷ 15 = 4 The answer is $4 per kilogram.
   Full step-by-step solution

   Step 1: Total cost = $60 Step 2: Total weight = 15 kilograms Step 3: Unit price = Total cost ÷ Total weight = 60 ÷ 15 Step 4: 60 ÷ 15 = 4 The answer is $4 per kilogram.

2. A rectangular prism is drawn with dimensions 12 cm by 8 cm by 5 cm. If you were to paint all the outside surfaces of this prism, what total surface area would you cover in square centimeters? Answer: 392 Solution: Identify the dimensions: length = 12 cm, width = 8 cm, height = 5 cm Calculate area of front and back faces: 2 × (12 × 5) = 2 × 60 = 120 cm² Calculate area of left and right faces: 2 × (8 × 5) = 2 × 40 = 80 cm² Calculate area of top and bottom faces: 2 × (12 × 8) = 2 × 96 = 192 cm² Add all…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 12 cm, width = 8 cm, height = 5 cm Step 2: Calculate area of front and back faces: 2 × (12 × 5) = 2 × 60 = 120 cm² Step 3: Calculate area of left and right faces: 2 × (8 × 5) = 2 × 40 = 80 cm² Step 4: Calculate area of top and bottom faces: 2 × (12 × 8) = 2 × 96 = 192 cm² Step 5: Add all areas: 120 + 80 + 192 = 392 cm² The answer is 392.

3. Aroha earns $1,701 for working 63 hours. What is her hourly wage? Answer: 27 Solution: Total earnings = $1,701 Total hours worked = 63 Hourly wage = 1701 ÷ 63 63 × 27 = 1701, so 1701 ÷ 63 = 27 The answer is $27 per hour.
   Full step-by-step solution

   Step 1: Total earnings = $1,701 Step 2: Total hours worked = 63 Step 3: Hourly wage = 1701 ÷ 63 Step 4: 63 × 27 = 1701, so 1701 ÷ 63 = 27 The answer is $27 per hour.

4. A factory produces 2,400 units of a product in 8 hours using 6 machines. If the factory needs to produce 5,400 units and can only run for 9 hours, how many machines will they need to operate at the same rate? Answer: 12 Solution: Find the production rate per machine per hour. Total production: 2,400 units Time: 8 hours Number of machines: 6 Production rate for all machines = 2,400 units ÷ 8 hours = 300 units/hour Production rate per machine = 300 units/hour ÷ 6 machines = 50 units per machine per hour Calculate how many…
   Full step-by-step solution

   Step 1: Find the production rate per machine per hour. Total production: 2,400 units Time: 8 hours Number of machines: 6 Production rate for all machines = 2,400 units ÷ 8 hours = 300 units/hour Production rate per machine = 300 units/hour ÷ 6 machines = 50 units per machine per hour Step 2: Calculate how many units need to be produced per hour for the new order. New production goal: 5,400 units Available time: 9 hours Required hourly production = 5,400 units ÷ 9 hours = 600 units/hour Step 3: Determine how many machines are needed. Each machine produces 50 units per hour Number of machines needed = 600 units/hour ÷ 50 units per machine per hour = 12 machines The factory will need to operate 12 machines.

5. Liam is planning a road trip and needs to calculate his fuel costs. His car can travel 315 miles on 15 gallons of gasoline. If gasoline costs $3.80 per gallon, how much will it cost Liam to drive 840 miles? Answer: $152 Solution: Find the car's fuel efficiency (miles per gallon). The car travels 315 miles on 15 gallons. Miles per gallon = 315 / 15 315 / 15 = 21 So the car gets 21 miles per gallon.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the car's fuel efficiency (miles per gallon).** The car travels 315 miles on 15 gallons. Miles per gallon = 315 / 15 315 / 15 = 21 So the car gets 21 miles per gallon. --- **Step 2: Find gallons needed for 840 miles.** Gallons = Total miles / Miles per gallon Gallons = 840 / 21 840 / 21 = 40 So Liam needs 40 gallons. --- **Step 3: Find total cost.** Gasoline costs $3.80 per gallon. Cost = Gallons × Price per gallon Cost = 40 × 3.80 40 × 3.80 = 152.00 --- **Final Answer:** $152

6. Mason earns $1,872 for working 72 hours. What is his unit rate of pay per hour? Answer: 26 Solution: Identify the total earnings: $1,872 Identify the total hours worked: 72 hours To find the unit rate (dollars per hour), divide the total earnings by the total hours: 1872 ÷ 72 Perform the division: 1872 ÷ 72 = 26 The unit rate is $26 per hour.
   Full step-by-step solution

   Step 1: Identify the total earnings: $1,872 Step 2: Identify the total hours worked: 72 hours Step 3: To find the unit rate (dollars per hour), divide the total earnings by the total hours: 1872 ÷ 72 Step 4: Perform the division: 1872 ÷ 72 = 26 Step 5: The unit rate is $26 per hour. The answer is 26.

7. A triangular prism is drawn with a triangular base that is a right triangle. The triangle's legs measure 6 cm and 8 cm, and the prism's length is 15 cm. What is the volume of the prism in cubic centimeters? Answer: 360 Solution: Find the area of the triangular base. The formula for the area of a right triangle is (1/2) * leg1 * leg2. Area = (1/2) * 6 cm * 8 cm Area = (1/2) * 48 cm² Area = 24 cm² Find the volume of the prism.
   Full step-by-step solution

   Step 1: Find the area of the triangular base. The formula for the area of a right triangle is (1/2) * leg1 * leg2. Area = (1/2) * 6 cm * 8 cm Area = (1/2) * 48 cm² Area = 24 cm² Step 2: Find the volume of the prism. The formula for the volume of a prism is area of base * length. Volume = 24 cm² * 15 cm Volume = 360 cm³ The volume of the prism is 360 cubic centimeters.