Question

A collection contains 8 paintings, 5 sculptures and some blue scarves which make up 1/3 of the total items. What percentage of the items are sculptures?

Answer 1

To determine the percentage of items that are sculptures, we start by defining the total number of items in the collection.

Let the number of blue scarves be \( x \). According to the information given, blue scarves make up \( \frac{1}{3} \) of the total items.

The total number of items can be expressed as:
\[
\text{Total items} = \text{paintings} + \text{sculptures} + \text{scarves} = 8 + 5 + x = 13 + x
\]

Since blue scarves account for \( \frac{1}{3} \) of the total items, we can write the following equation:
\[
x = \frac{1}{3} \times (13 + x)
\]

Multiplying both sides by 3 to eliminate the fraction:
\[
3x = 13 + x
\]

Now, we can solve for \( x \) by isolating it:
\[
3x - x = 13
\]
\[
2x = 13
\]
\[
x = \frac{13}{2} = 6.5
\]

Now we know that the number of blue scarves is 6.5. Let's calculate the total number of items:
\[
\text{Total items} = 8 + 5 + 6.5 = 19.5
\]

Next, we find the number of sculptures:
- There are 5 sculptures.

We need to find the percentage of items that are sculptures:
\[
\text{Percentage of sculptures} = \left( \frac{\text{Number of sculptures}}{\text{Total items}} \right) \times 100
\]
\[
\text{Percentage of sculptures} = \left( \frac{5}{19.5} \right) \times 100 \approx 25.64\%
\]

Therefore, approximately \( 25.64\% \) of the items are sculptures.