Challenging Whole Numbers Word Problems

1. Word Problem (10 pts)

A factory can produce 15,000 widgets per month. If the demand for the widgets increases by 20% each month, how many widgets will the factory need to produce in the third month to meet the demand? Show your working.

✎ Worked Solution

Step 1: Calculate the increase in demand for the first month: 15,000 × 0.20 = 3,000

Step 2: Calculate the total demand for the second month: 15,000 + 3,000 = 18,000

Step 3: Calculate the increase in demand for the second month: 18,000 × 0.20 = 3,600

Step 4: Calculate the total demand for the third month: 18,000 + 3,600 = 21,600

Answer: 21,600 widgets

2. Word Problem (10 pts)

A large cargo ship has a capacity of 8,000,000 kilograms. If each container weighs 120,000 kilograms and the ship is 80% loaded, how many containers are on the ship? Show your working.

✎ Worked Solution

Step 1: Calculate the loaded weight: 8,000,000 × 0.80 = 6,400,000 kg

Step 2: Calculate the number of containers: 6,400,000 ÷ 120,000 = 53.33

Step 3: Since only whole containers can be loaded, round down to the nearest whole number.

Answer: 53 containers

3. Word Problem (10 pts)

A classroom has 30 students, and each student needs 5 textbooks for different subjects. Two textbooks out of the required 5 were not available initially. If the school is now providing the remaining textbooks, how many textbooks are being distributed? Show your working.

✎ Worked Solution

Step 1: Calculate the total number of textbooks needed per student: 5 textbooks

Step 2: Subtract the unavailable textbooks: 5 - 2 = 3 textbooks

Step 3: Calculate the total number of textbooks distributed: 30 × 3 = 90

Answer: 90 textbooks

4. Word Problem (10 pts)

A gardener plants rows of trees with each row containing 48 trees. She plans to plant 5 such rows but removes 8 trees from the last row. How many trees does she plant in total? Show your working.

✎ Worked Solution

Step 1: Calculate the total number of trees in 5 full rows: 5 × 48 = 240

Step 2: Adjust for the 8 trees removed: 240 - 8 = 232

Answer: 232 trees

5. Word Problem (10 pts)

A bus travels 120 km in 1.5 hours. If it maintains the same speed, how far will it travel in 5 hours? Show your working.

✎ Worked Solution

Step 1: Calculate the speed of the bus: 120 ÷ 1.5 = 80 km/h

Step 2: Calculate the distance for 5 hours: 80 × 5 = 400 km

Answer: 400 km

6. Word Problem (10 pts)

A company packages juice in boxes, each box containing 24 bottles. The company receives an order for 50 boxes, but later the buyer cancels 10 boxes. How many bottles are in the final order? Show your working.

✎ Worked Solution

Step 1: Calculate the initial number of bottles: 50 × 24 = 1,200

Step 2: Calculate the reduction due to cancellation: 10 × 24 = 240

Step 3: Calculate the final number of bottles: 1,200 - 240 = 960

Answer: 960 bottles

7. Word Problem (10 pts)

A train travels at a speed of 72 km/h and needs to cover a distance of 648 km. How long will it take the train to complete the journey? Show your working.

✎ Worked Solution

Step 1: Use the formula Time = Distance / Speed

Step 2: Calculate the time required: 648 ÷ 72 = 9 hours

Answer: 9 hours

8. Word Problem (10 pts)

A tank can hold 4,500 liters of water. If 1/5 of the tank is empty, how much water is currently in the tank? Show your working.

✎ Worked Solution

Step 1: Calculate the empty portion of the tank: 4,500 × 1/5 = 900 liters

Step 2: Calculate the filled portion: 4,500 - 900 = 3,600 liters

Answer: 3,600 liters

9. Word Problem (10 pts)

If 9 labourers can finish a job in 12 days, how many days will it take for 6 labourers to finish the same job, assuming they work at the same rate? Show your working.

✎ Worked Solution

Step 1: Calculate the total amount of labour necessary (men-days): 9 × 12 = 108 men-days

Step 2: Calculate the number of days required for 6 labourers: 108 ÷ 6 = 18

Answer: 18 days

10. Word Problem (10 pts)

A car dealership offers two types of financing: 5% simple interest for 2 years or 3% simple interest for 4 years. If a customer plans to make a purchase of 5,00,000, which financing option requires them to pay less interest? Show your working.

✎ Worked Solution

Step 1: Calculate the interest for the first option: 5,00,000 × 0.05 × 2 = 50,000

Step 2: Calculate the interest for the second option: 5,00,000 × 0.03 × 4 = 60,000

Step 3: Compare the interest amounts.

Answer: The first option requires less interest (50,000 vs 60,000).