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She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked bot

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith?

Assumptions:

  • Let b be the number of hours Giselle worked as a blacksmith
  • Let c be the number of hours Giselle worked as a carpenter
Givens:
  • b + c = 30
  • 25b + 20c = 690
    • Rearrange equation (1) to solve for b by subtracting c from each side:
  • b = 30 - c
  • 25b + 20c = 690
    • Substitute equation (1) into equation (2) for b
    25(30 - c) + 20c = 690

    Multiply through:
    750 - 25c + 20c = 690

    To solve for c, we type this equation into our search engine and we get:
    c = 12

    Now, we plug in c = 12 into modified equation (1) to solve for b:
    b = 30 - 12
    b = 18

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    Patria Henriques

    Update: 2024-05-12

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