Answer this using decimals:Shirin receives money from her grandfather on her birthday. She first goes and gets a haircut for a quarter of the money, then she buys a shirt that costs SEK 260. Her little brother gets two-fifths of the money that is then left. Then she has SEK 60 left. How much money does she get from her grandfather

Let's denote the total amount of money Shirin receives from her grandfather as \( x \).

1. **Haircut Expense**: She spends a quarter of the money on a haircut, which is:
   \[
   \text{Haircut cost} = \frac{1}{4}x
   \]

   Therefore, the remaining amount after the haircut is:
   \[
   \text{Remaining amount} = x - \frac{1}{4}x = \frac{3}{4}x
   \]

2. **Shirt Expense**: She buys a shirt that costs SEK 260. The remaining amount after buying the shirt is:
   \[
   \text{Remaining amount after shirt} = \frac{3}{4}x - 260
   \]

3. **Money Given to Brother**: She gives her little brother two-fifths of the remaining amount. Thus, the amount given to her brother is:
   \[
   \text{Brother's share} = \frac{2}{5} \left( \frac{3}{4}x - 260 \right)
   \]

   After giving her brother this amount, she has SEK 60 left:
   \[
   \frac{3}{4}x - 260 - \frac{2}{5} \left( \frac{3}{4}x - 260 \right) = 60
   \]

Let's solve this equation step-by-step.

### Step-by-Step Solution:

1. Simplify the equation:

\[
\frac{3}{4}x - 260 - \frac{2}{5} \left( \frac{3}{4}x - 260 \right) = 60
\]

2. Distribute the fraction inside the parentheses:

\[
\frac{3}{4}x - 260 - \left( \frac{2}{5} \cdot \frac{3}{4}x - \frac{2}{5} \cdot 260 \right) = 60
\]

\[
\frac{3}{4}x - 260 - \left( \frac{3}{10}x - 104 \right) = 60
\]

3. Combine like terms:

\[
\frac{3}{4}x - \frac{3}{10}x - 260 + 104 = 60
\]

4. Find a common denominator for the fractions:

\[
\left( \frac{15}{20}x - \frac{6}{20}x \right) - 156 = 60
\]

\[
\frac{9}{20}x - 156 = 60
\]

5. Add 156 to both sides:

\[
\frac{9}{20}x = 216
\]

6. Solve for \( x \):

\[
x = 216 \cdot \frac{20}{9}
\]

\[
x = 480
\]

### Answer:

Shirin receives **SEK 480** from her grandfather.

Would you like any further details or clarifications? Here are a few related questions:

1. How much did Shirin spend on her haircut?
2. How much did Shirin have left after buying the shirt?
3. What fraction of the total money did Shirin give to her brother?
4. How much money did Shirin give to her brother in SEK?
5. What is the total percentage of the money Shirin spent?

**Tip:** When solving problems with fractions and percentages, converting everything into decimals can often simplify calculations.

Learn how to calculate the amount of money Shirin receives on her birthday using decimals with a detailed step-by-step solution. This problem covers key mathematical concepts such as fractions and equations in a real-life money scenario. Suitable for students in Grades 5-6.

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