SOLUTION: A singer has twice as many pants as she does shoes. She has three halves as many t shirts as she does pants. What is the least amount of items she can have to have a different wa

Question 33520: A singer has twice as many pants as she does shoes. She has three halves as many t shirts as she does pants. What is the least amount of items she can have to have a different wardrobe for each day of the year?
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
Hello!
From your problem, it's clear that, among the three items (shoes, t shirts and pants), the item of which she has less quantity is shoes. The sentence "A singer has twice as many pants as she does shoes" implies that shes has more pants than shoes. The following sentence "She has three halves as many t shirts as she does pants" implies that she has more t shirts than pants.

Since she has less shoes than any of the other two items, we have to use shoes as the basis to find the least total amount of items. In a year, there are 365 days. Therefore, in order to have a different wardrobe everyday, she needs at least 365 pairs of shoes, or 365*2 = 730 shoes; otherwise, she would need to wear the same pair of shoes on two different days.

We also know that she has twice as many pants as she does shoes. Since she has 730 shoes, then she also has 730*2 = 1460 pants.

Finally, she has 3/2 as many t shirts as she does pants. Therefore, she has 1460*3/2 = 2190 t shirts.

The total amount of items she has is 730 + 1460 + 2190 = 4,380.

I hope this helps!
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