1. **Problem statement:** A seamstress charges a bride 2180 including 23% VAT for a wedding dress. The materials were purchased including 23% VAT. The labour charge is twice the materials cost (before tax). Find the materials cost before tax, rounded to the nearest euro.
2. **Define variables:** Let $M$ be the materials cost before VAT.
3. **Calculate materials cost including VAT:** Materials cost including VAT is $M + 0.23M = 1.23M$.
4. **Labour cost:** Labour charge is twice the materials cost before tax, so labour cost = $2M$ (no VAT added here since the problem states the total includes VAT already).
5. **Total cost including VAT:** Total = materials cost including VAT + labour cost including VAT.
Since labour is charged twice the materials cost before tax, and the total includes VAT, labour cost including VAT = $2M \times 1.23 = 2.46M$.
6. **Equation for total price:**
$$
1.23M + 2.46M = 2180
$$
7. **Simplify:**
$$
(1.23 + 2.46)M = 2180
$$
$$
3.69M = 2180
$$
8. **Solve for $M$:**
$$
M = \frac{2180}{3.69}
$$
9. **Calculate:**
$$
M \approx 590.24
$$
10. **Round to nearest euro:**
$$
\boxed{590}
$$
This is the materials cost before tax.
Materials Cost Aadffe
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