Question 137388
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. 
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Original class numbers:
Total = "x"
Boys = 0.6x
Girls= 0.4x
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After 6-girls move and are replace by 6 boys:
Total = "x"
Boys:= 0.6x+6 = 0.75x

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Boys equation shows:
0.6x + 6 = 0.75x
6 = 0.15x
x = 40 (number in the class on the 1st day)
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2)An express and local train leave GraysLake at 3 P.M. and head for Chicago 50 miles away.
The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

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Express DATA:
Distance = 50 miles :  Rate = 2x mph ; time = 50/2x 
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Local train DATA:
Distance = 50 miles ; Rate = x mph ; time = 50/x
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EQUATION:
local train time - express train time = 1 hr
50/x - 50/2x = 1
Multiply thru by 2x to get:
100 - 50 = 2x
50 = 2x
x = 25 mph ( speed of the local train)
2x = 50 mph ( speed of the express)
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Cheers,
Stan H.