SOLUTION: 1. Find two numbers whose sum is 158 and whose difference is 14. (using the Diophantine equation model) 2. Find two numbers whose sum is 943 and whose difference is 429. (using

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Question 1074768: 1. Find two numbers whose sum is 158 and whose difference is 14. (using the Diophantine equation model)
2. Find two numbers whose sum is 943 and whose difference is 429. (using the Diophantine equation model)
3. John and James make a bet. If John loses, he must give James 30 marbles, and James will then have twice as many as John will. But if John wins, then James must give him 50 marbles, and then John will have three times as many as James will. How many marbles does each boy have to begin with?
4. Problem 27 in Diophantus' Arithmetica is to find two numbers when you know their sum and product. For example, the sum is 20 and the product is 96. Find the numbers. (use the Diophantine model)
5. Find two numbers whose sum is 30 and whose product is 216. (use the Diophantine model)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52824)   (Show Source): You can put this solution on YOUR website!
.
It is for the first time in my life I see these words "Diophantine equation model".

To check myself, I asked GOOGLE with these keywords.

Below see the GOOGLE response.

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Your search - "Diophantine equation model" - did not match any documents.

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Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

1. Find two numbers whose sum is 158 and whose difference is 14. (using the Diophantine equation model)
2. Find two numbers whose sum is 943 and whose difference is 429. (using the Diophantine equation model)
3. John and James make a bet. If John loses, he must give James 30 marbles, and James will then have twice as many as John will. But if John wins, then James must give him 50 marbles, and then John will have three times as many as James will. How many marbles does each boy have to begin with?
4. Problem 27 in Diophantus' Arithmetica is to find two numbers when you know their sum and product. For example, the sum is 20 and the product is 96. Find the numbers. (use the Diophantine model)
5. Find two numbers whose sum is 30 and whose product is 216. (use the Diophantine model) 
Why do you think you should DUMP all these questions on here for someone to do for you? 

Do you think you should attempt to do any of them, like 1, 2, 3, or 4? A person can do 1 for you, but why should they do all 5? Think about it!! 

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