During a public participation gathering, there were 4x women, 8y men and 160 youths. The number of men was 120 less than that of women. In total, 600 people attended the meeting
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We are told:
Number of women = 4x
Number of men = 8y
Number of youths = 160
The number of men was 120 less than women:
8y = 4x − 120
Total number of people = 600:
4x + 8y + 160 = 600
Step 1: Use the first equation to express one variable
We have:
8y = 4x −120
y = 4x−120
8
y = x - 30 OR y = x/2 - 15
2
Step 2: Substitute into the total equation
Total equation: 4x + 8y + 160 = 600
Substitute y= x/2 −15
4x + 8(x/2 − 15) + 160 = 600
Simplify:
4x + 4x − 120 + 160 = 600
8x + 40 = 600
8x = 560
x=70
Step 3: Find y
y = x/2 − 15
y = 70/2 − 15
y = 35 −15 = 20
y = 20
Step 4: Find the number of men
Number of men = 8y = 8 × 20 = 160
Final Answers:
x = 70, y = 20x
Number of men = 160
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