A singer has twice as many pants as pairs of shoes in her wardrobe and three-halves as many T-shirts as pants. What is the least number of items she can have in her wardrobe in order to make a different shoes, pants, and T-shirt combination for each year.
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Verified answer
Let s be the number of shoes. Then the number of pants is 2s. The number of t-shirts is three-halves the number of pants, or (3/2)(2s) = 3s.
The different combinations of a shirt, pair of pants, and pair of shoes is s * 2s * 3s = 6s^3. This has to be greater than or equal to 365, the number of days in a year. So we have
6s^3 > = 365
This is
s^3 >= 365/6
s > = (365/6)^(1/3), which is about 3.93
So the smallest integer s can be is 4. Therefore, she needs at least 4 pairs of shoes, 8 pairs of pants, and 12 shirts. On a side note, this works for a leap year too.
She has "s" shoes
She has "2s" pants.
She has "3/2 x 2s" T-shirts
....and you have asked an un-answerable question.
I know you all have tender psychies and all that stuff.... but couldn't you (at least) proof-read before you hit "select" or "enter" or whatever?