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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
- psunucLv 5il y a 1 décennieRéponse 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