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Simple and simultaneous equations sheet
Essay frame

A garment factory makes shirts and trousers. It must make 500 garments in total, using exactly 18,000 machine minutes. A shirt takes 30 minutes and a pair of trousers 45 minutes. How many of each should it make?

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Name the unknowns. Let s = shirts and t = trousers.
  2. 2 · Write the two equations.
    • Garments: s + t = 500.
    • Machine minutes: 30s + 45t = 18,000.
  3. 3 · Substitute. s = 500 − t, so 30(500 − t) + 45t = 18,000, giving 15,000 + 15t = 18,000.
  4. 4 · Solve. 15t = 3,000, so t = 200 and s = 500 − 200 = 300.
  5. 5 · Check in both conditions. 300 + 200 = 500 ✓; 30 × 300 + 45 × 200 = 9,000 + 9,000 = 18,000 ✓.
  6. 6 · Business link. The plan uses every machine minute, so no paid machine time is wasted.
  7. 7 · State the answer. 300 shirts and 200 pairs of trousers.