Susan has 10 pockets and 44 dollar bills. She wants to arrange the money so that there are a different number of dollars in each pocket. Can she do it? Explain.

Question

Mathematics

Tyshawn Pena

7 December, 01:38

Susan has 10 pockets and 44 dollar bills. She wants to arrange the money so that there are a different number of dollars in each pocket. Can she do it? Explain.

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Answers (1)

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Andreas Moreno · Answer 1

No

Step-by-step explanation:

The answer is no because no pocket can be empty and there isn't enough money to satisfy the condition. At least, one dollar must be stored in each pocket but the number (integer) of dollars in each pocket is different.

Let's store the minimum amount of dollars in the pockets while satisfying the condition. Place 1 dollar in the first pocket. The second pocket must have 2 dollars (it can't be 1 dollar, it must be a different number of dollars). The third pocket must have third dollars.

Repeating this process, the ninth pocket must have 9 dollars. At this moment, we have arranged 1+2+3+4+5+6+7+8+9=45 dollars in our pockets. But we only had 44 dollars! Plus, the tenth pocket is still empty.

If you store more dollars on the first, second, nth pockets, you will just run out of money more quickly than in our process above. so it's impossible to arrange the money in such way.