Asinger 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 clothing items she must have in her wardrobe in order to make different shoes, pants, and t-shirt combination each day of the year?

24

Step-by-step explanation:

Lets call p the total number of pants, s the number of pairs of shoes, and t the number of t-shirts. We have:

She can make each combination of clothing by selecting one pant, one pair of shoes and one t-shirt. Therefore, we know

As a result, she has a total of 2*s*s*3*s = s³*6 possibilities to choose. If she wants to make different combinations for an entire year, then 6s³ ≥ 366, as a result, s³ ≥ 61, so s ≥ ∛61 = 3.93

Since the number of clohes she has for each kind must be an integer, we know that s, 2*s and 3*s must be all integers, thus s must be at least 4.

As a verification, if she has 4 pair of shoes, then she must have 8 pants, and therefore 12 t-shirts, giving her a total of 4*8*12 = 384 possibilities. If she had just 3 pair of shoes, then she must had 6 pants and 9 t-shirts, and the total amount of possibilities might be only 3*6*9 = 162. Way below 365. We conclude that s = 4, p = 8, and t = 12.

The least number of clothes she must have should be 4+8+12 = 24

I hope this helped you!

$18 was the price of the t-shirt

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