Five friends

Five friends ate a 12-slice pizza. Samir ate three times as many slices as Joe. Joe ate half as many slices as Emily. Kendra and Fong together ate half a pizza. Kendra ate one-third as many slices as Samir. Fong ate the most slices. What fraction of a pizza did each person eat?

Correct answer:

S =  1/4
J =  1/12
M =  1/6
K =  1/12
F =  5/12

Step-by-step explanation:

S=3 J J=M/2 K+F=1/2 K=S/3 K+J+S+F+M=1  3JS=0 2JM=0 2F+2K=1 3KS=0 F+J+K+M+S=1  Pivot:Row1Row3 2F+2K=1 2JM=0 3JS=0 3KS=0 F+J+K+M+S=1  Row521 Row1Row5 2F+2K=1 2JM=0 3JS=0 3KS=0 J+M+S=0.5  Pivot:Row2Row3 2F+2K=1 3JS=0 2JM=0 3KS=0 J+M+S=0.5  Row332 Row2Row3 2F+2K=1 3JS=0 M+0.66667S=0 3KS=0 J+M+S=0.5  Row531 Row2Row5 2F+2K=1 3JS=0 M+0.66667S=0 3KS=0 M+1.33333S=0.5  Pivot:Row3Row4 2F+2K=1 3JS=0 3KS=0 M+0.66667S=0 M+1.33333S=0.5  Row5+Row4Row5 2F+2K=1 3JS=0 3KS=0 M+0.66667S=0 2S=0.5  S=20.5=0.25 M=100.66666666666667S=100.66666667 0.25=0.16666667 K=30+S=30+0.25=0.08333333 J=30+S=30+0.25=0.08333333 F=212K=212 0.08333333=0.41666667  F=1250.416667 J=1210.083333 K=1210.083333 M=610.166667 S=41=0.25

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