SOLUTION: If 40% of the students in Art Club were boys at beginning of the year, and in the middle of the year, 25% of the girls left, but 8 boys joined, leaving 42 students in the Art Club,

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: If 40% of the students in Art Club were boys at beginning of the year, and in the middle of the year, 25% of the girls left, but 8 boys joined, leaving 42 students in the Art Club,      Log On


   



Question 1055681: If 40% of the students in Art Club were boys at beginning of the year, and in the middle of the year, 25% of the girls left, but 8 boys joined, leaving 42 students in the Art Club, what was the total amount of students to begin with?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the total number
of students to begin with
+.4x+ = number of boys at beginning
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+x+-+.4x+=+.6x+ = number of
girls at beginning
25% of the girls left, so 75% are left
+.75%2A.6x+=+.45x+ = number of
girls remain
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+8+ boys joined, so there are now
+.4x+%2B+8+ boys
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+42+ students are left, so
+%28+.45x+%29+%2B+%28+.4x+%2B+8+%29+=+42+
+.85x+%2B+8+=+42+
+.85x+=+34+
+x+=+40+
There were 40 students to begin with
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check:
40% of 40, or 16 students were boys at start
40 - 16 = 24 were girls
25% of the girls left, or 6 girls
That left 24 - 6 = 18 girls remaining
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8 boys joined, making 16 + 8 = 24 boys
18 + 24 = 42 students remaining
OK