If A+B=Z, Z+P=T, T+A=F, B+P+F=100, and A=8, then what is the value of F?

z+P=T and B+P+F=100

make P subject

P=T-Z and P=100-B-F

simplify T-Z=100-B-F

but we know Z=A+B, substitute for Z in above equation

so T-A-B=100-B-F

hence T-A=100-F

but A=8

so equation will be T+F=108

also we know T+A=F

implying T-F=-8

soving the two by elimination

T+F=108

T-F=-8

2T=100

T=50

so F=58

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