You are an AI Assistant.
system
On a shopping trip, Jill spent 50 percent of her total amount on clothing, 20 percent on food, and a certain percentage on other items. She paid a 5 percent tax on the clothing, no tax on the food, and a 10 percent tax on all other items. The total tax that she paid was 5.5 percent of the total amount that she spent, excluding taxes. What percentage of her total amount did Jill spend on other items?
user
Let's denote the total amount Jill spent as \( T \).

She spent 50% on clothing, which is \( 0.50T \).
She spent 20% on food, which is \( 0.20T \).
Let's denote the percentage she spent on other items as \( x \), so she spent \( xT \) on other items.

The total amount spent on clothing, food, and other items is \( T \), so we have:
\[ 0.50T + 0.20T + xT = T \]
\[ 0.70T + xT = T \]
\[ xT = T - 0.70T \]
\[ xT = 0.30T \]
So, \( x = 0.30 \) or 30%.

Now, let's calculate the taxes she paid on each category:
- Tax on clothing: 5% of 50% of \( T \) is \( 0.05 \times 0.50T = 0.025T \).
- Tax on food: 0% of 20% of \( T \) is \( 0 \times 0.20T = 0T \).
- Tax on other items: 10% of 30% of \( T \) is \( 0.10 \times 0.30T = 0.03T \).

The total tax paid is the sum of these taxes:
\[ \text{Total tax} = 0.025T + 0T + 0.03T \]
\[ \text{Total tax} = 0.055T \]

We are given that the total tax paid is 5.5% of the total amount spent excluding taxes, which is \( T \). So we have:
\[ 0.055T = 0.055T \]

This confirms that the total tax paid is indeed 5.5% of the total amount spent, and Jill spent 30% of her total amount on other items.
assistant