Answer:
24
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:
- p = 2*s
- t = 1.5*p = 1.5*(2*s) = 3*s
She can make each combination of clothing by selecting one pant, one pair of shoes and one t-shirt. Therefore, we know
- She has as many possibilities of selecting pants as the amount of pants she has, thus she has 2*s possibilities.
- She has s possibilities to pick a pair of shows
- She has 3*s possibilities to pick a t-shirt.
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!