Alex has 395 cards. Michael has 250 cards. They both give the same number of cards to their friend Austin. After giving cards to Austin, the numbers of cards Alex has is less than two times the amount of cards Michael has. Write and solve an inequality to determine the range of cards they gave Austin. (Write your answer in a complete sentence.)

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1 Answer

395-x<2(250-x), where x is the number of cards they each give Austin,




In words:

If x is the number of cards Austin gets from each of Alex and Michael, Austin gets 2x cards altogether. Alex has 395-x cards left while Michael has 250-x cards left. Alex now has less than twice as many as cards as Michael. Twice the number of cards Michael has is 500-2x, and Alex has less than this. This means that, if Alex were now to receive the number of cards Austin received in total, he would have 395+x cards, which is less than 500 cards. Therefore, the number of cards they each gave Austin must be less than 105. This means that Austin received an even number of cards which is less than twice this, that is, 210 cards. We know he received some cards, so the minimum is 2 (one from Alex and one from Michael) and a maximum of 208 (104 from each of the others).

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