There were 204 participants from the three schools
<h3>How to determine the number of participants?</h3>
The given parameters are:
X = 12 + Y
X = Z - 18
Girls = Boys + 50
The ratios of the number of boys to girls in the schools are:
1 : 2
1 : 5
2 : 1
This means that:
- School X: Boys = 1/3 and Girls = 2/3
- School Y: Boys = 1/6 and Girls = 5/6
- School Z: Boys = 2/3 and Girls = 1/3
So, we have:
Boys = 1/3X + 1/6Y + 2/3Z
Girls = 2/3X + 5/6Y + 1/3Z
Substitute the above equations in Girls = Boys + 50
2/3X + 5/6Y + 1/3Z = 1/3X + 1/6Y + 2/3Z + 50
Evaluate the like terms
1/3X + 2/3Y - 1/3Z = 50
Multiply through by 3
X + 2Y - Z = 150
So, we have:
X = 12 + Y
X = Z - 18
X + 2Y - Z = 150
Substitute X = 12 + Y in X = Z - 18 and X + 2Y - Z = 150
12 + Y = Z - 18 ⇒ Y - Z = 30
12 + Y + 2Y - Z = 150 ⇒ 3Y - Z = 138
Subtract Y - Z = 30 from the equation 3Y - Z = 138 to eliminate Z
2Y = 108
Divide by 2
Y = 54
Substitute Y = 54 in X = 12 + Y
X = 12 + 54
X = 66
Substitute X = 66 in X = Z - 18
66 = Z - 18
Solve for Z
Z = 66 + 18
Z = 84
So, the total number of participants from the 3 schools is
Total = X + Y + Z
This gives
Total = 66 + 54 + 84
Evaluate the sum
Total = 204
Hence, there were 204 participants from the three schools
Read more about system of equations at:
brainly.com/question/14323743
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