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We always liked poking around Grandpa's attic whenever we had a family reunion. We found all sorts of neat stuff up there. Once we found a bunch of baseball cards, so Grandpa said, "Just divide 'em up among all the grandchildren." There were 5040 cards in all, so each of us got a lot of cards. But then we remembered that the Yakliches, who had five of the grandchildren, hadn't arrived yet. So each of those of us present had to give up 75 cards so that all the grandchildren would have the same number of cards. How many grandchildren does grandpa have?

I have to use the guess and check method for this problem. I know by using algebra and setting up the problem there are going to be 21 grandchildren. I need help setting up the guess and check method to solve the problem.

I know what we will be guessing is the number of grandchildren but how do I use the rest of the information to solve this problem, and how do I set it up?

Samantha
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2 Answers2

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Let the number of grandchildren initially present is $x$. So the total number of grandchildren is $x+5$.

In the first attempt of distribution, $5040$ cards were divided equally among $x$ grandchildren.

Let $\large\frac{5040}{x}=y$. ...(I)

In the next attempt of distribution, $5040$ cards were divided among $x+5$ with each of the $x$ grandchildren having 75 cards less from the first attempt of distribution.

So, $\large\frac{5040}{x+5}=y-75$ ...(II)

Solve equation (I) and (II) to get the answer.

Vikram
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To guess and check, start with an initial estimate, say 10 total grandchildren. That means five children each gave up 75 cards and each of the Yakliches would get 75. Now check. Is 75 times 10 equal to 5040? No. It is only 750. We need many more grandchildren to get to the correct total. So try again. Start with 10 grandchildren already present. If they each give 75 cards (for a total of 750) to be split among the 5 Yaklich children, each child gets 150. Now there are 15 total grandchildren. 15 times 150 is 2250. Still not right. Keep guessing, increasing the number of children already there to find the correct number of total grandchildren.

Amber
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  • Since this is a two year old Question, I think it is unhelpful to post as an Answer a rambling and unpolished response that fails to include a solution. However this does seem to be in the spirit of the original problem, so I encourage you to revise it (Edit) and improve. – hardmath Aug 01 '16 at 21:37