A worker needs to pack 350kg of rice and 150kg of wheat in bags such that each bag weighs the same. Each bag should either contain rice or wheat. Which option shows the correct steps to find the greatest amount of rice/wheat the worker can pack in each bag?
Question
A worker needs to pack 350kg of rice and 150kg of wheat in bags such that each bag weighs the same. Each bag should either contain rice or wheat. Which option shows the correct steps to find the greatest amount of rice/wheat the worker can pack in each bag?
Solution
To find the greatest amount of rice/wheat the worker can pack in each bag, we need to determine the greatest common divisor (GCD) of 350kg and 150kg.
Step 1: Find the GCD of 350kg and 150kg.
- List the factors of 350kg: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
- List the factors of 150kg: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
- The common factors are: 1, 2, 5, 10, 25, 50.
- The greatest common factor is 50kg.
Step 2: Divide the weights of rice and wheat by the GCD.
- Divide 350kg of rice by 50kg: 350kg / 50kg = 7 bags of rice.
- Divide 150kg of wheat by 50kg: 150kg / 50kg = 3 bags of wheat.
Therefore, the worker can pack 7 bags of rice and 3 bags of wheat, with each bag weighing 50kg.
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