# Word problem

### Word problem

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Any help with this problem would be much appreciated
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Guest

### Re: Word problem

Let the number of seashells Allie, Bev, and Cheryl have be "A", "B", and "C", respectively.

"Allie gives Bev and Cheryl as many seashells as each of them then has."
So Allie gives Bev B shells and gives Cheryl C shells.
Allie now has A- B- C shells, Bev has 2B shells, and Cheryl has 2C shells.

"Then Bev gives Allie and Cheryl as many shells as each of them then has."
Bev gives Allie A- B- C shells and gives Cheryl 2C shells.
Allie now has 2(A- B- C)= 2A- 2B- 2C shells, Bev has 2B- (A- B- C)- 2C= 3B-A- C shells, and Cheryl has 4C shells.

"Finally, Cheryl gives Bev and Allie as many shells as each has."
So Cheryl gives Bev 3B- A- C shells and gives Allie 2A- 2B- 2C shells.
Allie now had 4A- 4B- 4C shells, Bev has 6B- 2A- 2C shells, and Cheryl has 4C- (3B- A- C)- (2A- 2B- 2C)= 7C- B- A shells.
"If they now have 24 shells each, how many shells did Bev have to start with?"
We have three equations
4A- 4B- 4C= 24
6B- 2A- 2C= 24 and
7C- B- A= 24

Trying to solve those, I got a negative answer for B so I must have done something wrong!
Guest

### Re: Word problem

No, solving that again, I get the same equations but they all have positive integer solutions.
Guest

### Re: Word problem

Thanks, you made it look easy
Guest