Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Algebra Linear Equation?

Laura the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 9 clients who did Plan A and 7 who did Plan B. On Thursday there were 3 clients who did Plan A and 5 who did Plan B. Laura trained her Wednesday clients for a total of 12 hours and her Thursday clients for a total of 6 hours. How long does each of the workout plans last?

Length of each Plan A workout:

Length of each Plan B workout: 

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  • 1 month ago

    Laura the trainer has two solo workout plans that she offers her clients: 

    Plan A and Plan B. Each client does either one or the other (not both). 

    On Wednesday there were 9 clients who did Plan A and 7 who did Plan B. 

    On Thursday there were 3 clients who did Plan A and 5 who did Plan B. 

    Laura trained her Wednesday clients for a total of 12 hours 

    and her Thursday clients for a total of 6 hours. 

    How long does each of the workout plans last?

    Create a system of equations 

    let A be the duration of a Plan A session and B be the duration of a Plan B session

    For Wednesday: 9A + 7B = 12 hours

    For Thursday: 3A + 5B = 6 hours

    Multiply the Thursday equation by 3 then solve the system through subtraction:

    9A + 7B = 12

    (3A + 5B = 6) * 3

    ----------------------

    8B = 6

     

    B = 0.75 hours

    plug that into one of the original equations:

    3A + 5(0.75) = 6

    3A = 2.25

    A = 0.75

     

    Length of each Plan A workout: 0.75 hours

    Length of each Plan B workout: 0.75 hours

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