Question 1: An engineer divides a total resource of 360 units among three departments in the ratio 2:3:5. Calculate the units allocated to each department.

Answer: 80, 120, 160

Question 2: A construction project allocates materials in the ratio 4:5:6 among foundation, framing, and finishing. If the total materials used are 1500 units, how many units go to each phase?

Answer: 400, 500, 600

Question 3: A bridge engineering team distributes budget in the ratio 7:2:5 for design, materials, and labor, respectively. If the total budget is $84,000, what is allocated to each?

Answer: $42,000, $12,000, $30,000

Question 4: Fluency & Practice: A factory divides its weekly output of 2100 units among three product lines in the ratio 3:4:5. Find the units assigned to each product line.

Answer: 350, 420, 630

Question 5: Problem Solving & Reasoning: An engineer has a total of 480 meters of cable to distribute among four segments in the ratio 1:2:3:4. How many meters does each segment get? Explain your steps.

Answer: Segment 1: 60m, Segment 2: 120m, Segment 3: 180m, Segment 4: 120m

Question 6: In an engineering project, materials are shared among three teams in the ratio 5:3:2. If Team A receives 50 units, what is the total amount of materials, and how much does each team get?

Answer: Total: 100 units; Team B: 30 units, Team C: 20 units

Question 7: Construct a diagram on the grid showing the sharing of 540 units among four parts in the ratio 1:2:3:4.

Answer: Parts: 1: 72, 2: 144, 3: 216, 4: 108

Question 8: A bridge supports a load split among three cables in the ratio 2:3:5. If the total load is 1000 kN, find the load on each cable.

Answer: 200 kN, 300 kN, 500 kN

Question 9: Challenge & Extension: A team of engineers shares 1200 liters of paint among four projects in the ratio 1:2:3:4. If Project 3 receives 300 liters, verify and find the amounts for all projects.

Answer: Ratios imply project 3: 3 parts = 300 liters, so 1 part = 100 liters; others: 100, 200, 400 liters

Question 10: Error Analysis: A student claims that sharing 900 units in the ratio 2:3:4 results in 300, 450, and 150 units. Is this correct? If not, identify and correct the mistake.

Answer: Incorrect; total parts = 2+3+4=9; each part = 100; shares: 200, 300, 400 units