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jacob s a posé la question dans Science & MathematicsMathematics · il y a 1 décennie

How many Kgs of each alloy should be taken to produce 600kg of new alloy that is 53.8%Cu,30.1%Zn & 3.2%Pb?

I have available 4 Bronze alloys containing the following percentages of Cu,Zn,and Pb.

Alloy 1 Alloy2 Alloy3 Alloy4

Copper 52 , 53 , 54 , 55

Zinc 30 , 38 , 20 , 38

lead 3.0, 2.0 , 4.0 , 3.0

2 réponses

Pertinence
  • psunuc
    Lv 5
    il y a 1 décennie
    Réponse favorite

    Because you have four alloys and only 3 target elements there is no definite solution (ie, there is more than one possibly answer) let A represent alloy 1, B alloy 2, C alloy 3, and D alloy 4

    This sets up a system of equations

    52A + 53B + 54C + 55D = 53.8 * 600

    30A + 38B + 20C + 38D = 30.1 * 600

    3A + 2B + 4C + 3D = 3.2*600

    one possible solution is

    A 205.477725

    B 72.66838138

    C 180.542751

    D 145.3530194

  • il y a 1 décennie

    You can write 4 equations in 4 variables using the information given.

    .52x+.53y+.54z +.55w=.538(600)

    .30x+.38y+.20z+.38w=.301(600)

    .03x+.02y+.04z+.03w=.032(600)

    1x+1y+1z+1w=600

    You can use multiplication, subtraction and substitution to solve this manually or take the coefficients of the variables to the website:

    http://graph.seriesmathstudy.com/ start the tool GraphFunc, select Linear Equations under the Functions drop down button. Put in the coefficients and values of the 4 equations and it will solve it for you. Your answers might need to rounded to the nearest whole number.

    Source(s) : Knowledge of ex mathematics teacher
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