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March 26, 2017

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A hardware supplier manufactures three kinds of clamps, type A, B, and C. Production restrictions force it to make 20 more type C clamps than the total of the other types and twice as many as B clamps as type A clamps. The shop must produce 380 clamps per day. How many of each type are made per day? How many type A clamps are produced?

  • ALGEBRA - ,

    "three kinds of clamps, type A, B, and C"
    Let A,B,C represent the number of each.

    "20 more type C clamps than the total of the other types"
    C=A+B+20

    "twice as many as B clamps as type A clamps."
    A=2B

    "produce 380 clamps per day"
    A+B+C=380

    So in summary, the equations are:
    A+B+C=380 ...(1)
    C=A+B+20 ...(2)
    A=2B ...(3)

    This can be solved by successive substitution as follows:

    A=2B => C=(2B)+B+20=3B+20
    Substitute A and C in the first equation
    (2B) + B + (3B+20) = 380
    Solve for B:
    6B=360
    B=60
    therefore
    A=2B = 120
    C=3B+20=200
    Check: A+B+C=120+60+200=380 OK.

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