1. A box contains a number of items, among them exactly 10 hats, 3 books, and 7 statues. The remaining 1/3 of the items are all blue T-shirts. What percent of the items in the box are books?

10 + 3 + 7 + 1/3x = x

20 = 2/3x

20/(2/3) = x

20 * (3/2) = x

60/2 = 30 = x

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3/30 = 0.1 = 10%

To find the percentage of items that are books, we first need to determine the total number of items in the box.

Let's start by finding the fraction of items that are books. We know that there are 10 hats, 3 books, and 7 statues. So, the fraction of items that are books is:

3 / (10 + 3 + 7)

Next, let's find the fraction of items that are blue T-shirts. We know that the remaining 1/3 of the items are blue T-shirts. So, the fraction of items that are blue T-shirts is:

1/3

To find the fraction of items that are books, we subtract the fraction of items that are blue T-shirts from 1:

1 - 1/3

Now, let's find the fraction of items that are books:

2/3

To convert the fraction into a percentage, we multiply it by 100:

(2/3) * 100

Calculating this, we find that 66.67% of the items in the box are books.

To find the percentage of the items in the box that are books, we need to know the total number of items in the box.

In the given information, we know that there are 10 hats, 3 books, and 7 statues, which make a total of 10 + 3 + 7 = 20 items.

Now, we need to find out how many items are blue T-shirts. It is stated that the remaining 1/3 of the items are blue T-shirts. So, if we subtract the number of hats, books, and statues from the total number of items, we can find the number of blue T-shirts.

Remaining items = Total items - (Hats + Books + Statues)
Remaining items = 20 - (10 + 3 + 7)
Remaining items = 20 - 20
Remaining items = 0

So, there are 0 blue T-shirts in the box.

Now, to find the percentage of items that are books, we can divide the number of books by the total number of items and multiply it by 100.

Percentage of books = (Number of books / Total number of items) * 100
Percentage of books = (3 / 20) * 100
Percentage of books = 0.15 * 100
Percentage of books ≈ 15

Therefore, approximately 15% of the items in the box are books.