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 define the amount of money Shirin receives from her grandfather as \( x \) SEK.

1. **Haircut Expense**: She spends a quarter of the total money on a haircut.
   \[
   \text{Amount spent on haircut} = \frac{1}{4}x
   \]
   After the haircut, the remaining money is:
   \[
   x - \frac{1}{4}x = \frac{3}{4}x
   \]

2. **Shirt Purchase**: She then buys a shirt for SEK 260.
   \[
   \text{Remaining money after buying the shirt} = \frac{3}{4}x - 260
   \]

3. **Brother's Share**: Her little brother receives two-fifths of the remaining money.
   \[
   \text{Money left after buying the shirt} = \frac{3}{4}x - 260
   \]
   \[
   \text{Brother's share} = \frac{2}{5}\left(\frac{3}{4}x - 260\right)
   \]
   The remaining money after giving her brother his share is SEK 60:
   \[
   \frac{3}{4}x - 260 - \frac{2}{5}\left(\frac{3}{4}x - 260\right) = 60
   \]

4. **Solving the Equation**:

   First, simplify the expression inside the parentheses:
   \[
   \frac{2}{5}\left(\frac{3}{4}x - 260\right) = \frac{6}{20}x - \frac{520}{5} = \frac{3}{10}x - 104
   \]

   Substitute this into the equation:
   \[
   \frac{3}{4}x - 260 - \left(\frac{3}{10}x - 104\right) = 60
   \]

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

   To combine the fractions, find a common denominator (which is 20):
   \[
   \frac{15}{20}x - \frac{6}{20}x - 156 = 60
   \]
   \[
   \frac{9}{20}x - 156 = 60
   \]

   Add 156 to both sides:
   \[
   \frac{9}{20}x = 216
   \]

   Solve for \( x \) by multiplying both sides by the reciprocal of \(\frac{9}{20}\):
   \[
   x = 216 \times \frac{20}{9}
   \]
   \[
   x = 480
   \]

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

---

Would you like more details, or do you have any questions?

Here are some related questions:

1. What would be the remaining amount if the shirt cost SEK 300 instead of SEK 260?
2. How much would her brother receive if Shirin had received SEK 600 from her grandfather?
3. What fraction of the total money does Shirin's brother get in terms of the remaining amount after the haircut and shirt purchase?
4. How much money would Shirin have left if she spent half of her total amount on a haircut instead of a quarter?
5. If Shirin received a 10% bonus from her grandfather, how much would she receive in total?

**Tip:** Always double-check calculations involving fractions and percentages to ensure accuracy, especially in financial contexts!

Explore the solution to a math problem involving Shirin's birthday money calculation. Understand how Shirin allocates her money for a haircut, shirt purchase, and her brother's share, with a final amount of SEK 480. Suitable for Grades 5-6.

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