Mayor voting calculation

In a particular village, two candidates ran for mayor. Candidate A was voted for by 70% of all voters, of whom 60% were women. Candidate B was voted for by all other voters and 20% of women from all participating voters. How many men voted for candidate B if 1022 men voted for candidate A?

Final Answer:

M =  365

Step-by-step explanation:


A = 1022+Z
Z = A · 0.60
A+B = N
A = 0.70·N
B = M+ 0.20·N

A-Z = 1022
0.6A-Z = 0
A+B-N = 0
A-0.7N = 0
B-M-0.2N = 0

Row 2 - 0.6 · Row 1 → Row 2
A-Z = 1022
-0.4Z = -613.2
A+B-N = 0
A-0.7N = 0
B-M-0.2N = 0

Row 3 - Row 1 → Row 3
A-Z = 1022
-0.4Z = -613.2
B-N+Z = -1022
A-0.7N = 0
B-M-0.2N = 0

Row 4 - Row 1 → Row 4
A-Z = 1022
-0.4Z = -613.2
B-N+Z = -1022
-0.7N+Z = -1022
B-M-0.2N = 0

Pivot: Row 2 ↔ Row 3
A-Z = 1022
B-N+Z = -1022
-0.4Z = -613.2
-0.7N+Z = -1022
B-M-0.2N = 0

Row 5 - Row 2 → Row 5
A-Z = 1022
B-N+Z = -1022
-0.4Z = -613.2
-0.7N+Z = -1022
-M+0.8N-Z = 1022

Pivot: Row 3 ↔ Row 5
A-Z = 1022
B-N+Z = -1022
-M+0.8N-Z = 1022
-0.7N+Z = -1022
-0.4Z = -613.2


Z = -613.2/-0.4 = 1533
N = -1022-Z/-0.7 = -1022-1533/-0.7 = 3650
M = 1022-0.8N+Z/-1 = 1022-0.8 · 3650+1533/-1 = 365
B = -1022+N-Z = -1022+3650-1533 = 1095
A = 1022+Z = 1022+1533 = 2555

A = 2555
B = 1095
M = 365
N = 3650
Z = 1533

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