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?

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

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.