Subjects algebra

Materials Cost Aadffe

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

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.