A shopkeeper paid $810 for some blouses and skirts. A blouse cost $20 and a skirt costs half the price of a blouse. If she bought 9 more skirts than blouses, how many skirts did she buy?

Let's denote the number of blouses the shopkeeper bought as $ b $ and the number of skirts as $ s $.

Given:
- The cost of a blouse is $20.
- The cost of a skirt is half the price of a blouse, which is $ \frac{20}{2} = 10 $ dollars.
- The total amount spent by the shopkeeper is $810.
- The shopkeeper bought 9 more skirts than blouses, so $ s = b + 9 $.

We can write the total cost equation as:
\[
20b + 10s = 810
\]

Substituting $ s = b + 9 $ into the equation:
\[
20b + 10(b + 9) = 810
\]

Simplifying the equation:
\[
20b + 10b + 90 = 810
\]
\[
30b + 90 = 810
\]

Subtracting 90 from both sides:
\[
30b = 720
\]

Dividing by 30:
\[
b = 24
\]

So, the shopkeeper bought 24 blouses. Since $ s = b + 9 $, the number of skirts is:
\[
s = 24 + 9 = 33
\]

Therefore, the shopkeeper bought **33 skirts**.

Would you like a detailed explanation, or do you have any questions?

Here are five related questions to further your understanding:
1. If the shopkeeper had bought 5 more blouses, how many skirts would she have bought?
2. What would be the total cost if the shopkeeper bought 10 fewer skirts?
3. If the price of each blouse increased by $5, how would the total cost change?
4. What if the shopkeeper had spent $1000 instead of $810, how many blouses and skirts could she have bought?
5. If the cost of a skirt doubled, how would that affect the number of skirts the shopkeeper could buy for the same $810?

**Tip:** When dealing with word problems, carefully translate the problem's conditions into equations. This method makes solving the problem more straightforward.

Learn how to calculate the number of skirts bought by a shopkeeper based on the cost of blouses and skirts. This problem involves solving linear equations and understanding the relationship between the costs and quantities of items purchased. Suitable for students in Grades 7-9.

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