Here is how the 7.11 problem is figured out simply, just by using the Quadratic Equation & Substitution...

a+b+c+d=7.11 and abcd=7.11
a+b+c=x and d=y
x+y=7.11
y=-x+y
-x2+7.11x-7.11=0
y=1.20
so d=1.20
a+b+c=5.91
abc=5.91
x+y=5.91
xy=5.91
y=-x+5.91
-x2+5.91x-5.91=0
x=1.28
so c=1.28
a+b=4.63
ab=4.63
b=-a+4.63
-a2+4.63x-4.63=0
a=3.17
b=4.63-3.17
b=1.46

then you can make 3 graphs
y=-x+7.11 & y=7.11/x
y=-x+5.91 & y=5.91/x
y=-x+4.63 & y=4.63/x

I see now how to apply your teacher's method. Very nice.

But a*b*c*d = 7.1089152, not 7.11...

-Dan

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Nice, that way is far more simple than my way. Although, I got:

$3.16, $1.25, $1.50, $1.20 for a, b, c, d respectively. You should get 7.11 exactly, as opposed to 7.1089152.

i dont understand your justification for saying that

a + b + c = a*b*c