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On the first day of school, the percentage of boys in a p...
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by
WinpossibleUser3743
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On the first day of school, the percentage of boys in a particular class is 60%. During the school year, six girls move away, and are replaced in the class by six boys; this makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school. - Determine how many solutions exist
- Use either elimination or substitution to find the solutions (if any)
- Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection
i understand how to get the answer i just dont understand how to make the answer meet the above requirments
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Responses
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Let the no. of boys in the class at the beginning of year be x
and the no. of girls in the class at the beginning of year be y
So as per the question
x/(x+y) *100 = 60
=> x/(x+y) = 0.60
=> x = 0.60(x+y)
=> 0.4x – 0.6y = 0 ….............Eq 1
=> x = 0.6y/0.4
During the year 6 girls left and 6 boys joined the class.
So, after this transition no. of boys in the class = x +6
and no. of girls = y - 6
Now as per the question percentage of boys in the class is 75
=> x+6/{(x+6) + (y -6)}*100 = 75
=> x+6/{x + y} = 0.75
=> x + 6 = 0.75 (x + y)
=> 0.25 x – 0.75 y = -6 …................Eq 2
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by
Winpossible
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Sep 08, 10 09:49AM PST
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More to the above response:
Now putting value of x from the equation 1 in the equation 2
=> 0.25{0.6y/0.4} – 0.75y = -6
=> 0.375y – 0.75y = -6
=> -0.375y = -6
=> y = 6 / 0.375 = 16
Now replacing the value of y in the equation 1
=> x = 0.6*16/ 0.4
=> x = 24
Hence, in the beginning of the year, there were 24 boys and 16 girls.
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by
Winpossible
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Sep 08, 10 09:50AM PST
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More to the above answer:
Now coming over to the second part of the question i.e. showing these two lines on the graph, for this we need to have at least two points on every line.
For line 1 ( 0.4x – 0.6y = 0 )
If we put x = 0, then y = 0 => Point (0, 0)
if we put x = 24, then y = 16 => Point (24, 16)
For line 2 (0.25 x – 0.75 y = -6 )
If we put x = 0, then y = 8 => Point (0, 8)
If we put x = 24, then y = 16 => Point (24, 16)
So, to draw these lines on the graph, first we have mark all the four points in the graph.
If we join (0, 0) and (24, 16) with the scale, this will represent line 0.4x – 0.6y = 0 and if we join (0, 8) and (24, 16), this will represent line 0.25 x – 0.75 y = -6.
Where these two lines intersect each other, that point will give us the solution of this question. As in this question these two line intersect at (24, 16), hence the solution of this question is x = 24 and y =16.
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by
Winpossible
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Sep 08, 10 10:58AM PST
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