Rei bought 150 oranges and 100 apples for her neighbours. She divided the oranges equally among them and had 17 oranges left. She also divided the apples equally among them and had 5 apples left. How many neighbours were there.
Question
Rei bought 150 oranges and 100 apples for her neighbours. She divided the oranges equally among them and had 17 oranges left. She also divided the apples equally among them and had 5 apples left. How many neighbours were there.
Solution
Sure, here's how you can solve this problem:
Step 1: First, subtract the number of leftover oranges from the total number of oranges Rei bought. This gives you 150 - 17 = 133 oranges.
Step 2: Then, subtract the number of leftover apples from the total number of apples Rei bought. This gives you 100 - 5 = 95 apples.
Step 3: Since Rei divided the oranges and apples equally among her neighbours, the number of neighbours is the greatest common divisor (GCD) of 133 and 95.
Step 4: To find the GCD of 133 and 95, you can use the Euclidean algorithm.
Step 5: The Euclidean algorithm is as follows:
- Subtract the smaller number from the larger number.
- Then replace the larger number with the result.
- Repeat the process until the numbers are equal. That will be your GCD.
Step 6: Using the Euclidean algorithm, you find that the GCD of 133 and 95 is 19.
So, Rei has 19 neighbours.
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