There are 364 first-grade students. If there are 26 more girls than boys, how many girls are there?
How to do this depends on whether you are in basic math or algebra.
I don't know which you are in, so I'll do it both ways:
1. BY BASIC MATH:
Suppose all the first graders are in the auditorium.
Suppose 26 girls leave the auditorium. Then there will be the
same number of girls as boys.
There will be 364-26 or 338 students left in the auditorium when
the 26 girls leave.
Half of those left in the auditorium are boys and half of them girls.
So there are 338÷2 or 169 boys and 169 girls.
Then if the other 26 girls return to the auditorium there will be 169+26
or 195 girls.
Answer: 195 girls.
Checking: 195 girls + 169 boys = 364 students.
girls.
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2. BY ALGEBRA (THREE WAYS)
FIRST WAY BY ALGEBRA:
there are 26 more girls than boys
Let the number of boys = B
Then
The number of girls = B+26
There are 364 first-grade students
Number of boys + Number of girls = 364 students
B + B+26 = 364
2B+26 = 364
2B = 338
B = 169 boys
The number of girls = B+26 = 169+26 = 195
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SECOND WAY BY ALGEBRA:
Let the number of girls = G
The number of boys = 364 - G
there are 26 more girls than boys
Number of girls = Number of boys + 26
G = 364-G + 26
G = 390-G
2G = 390
G = 195
There are 195 girls.
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THIRD WAY BY ALGEBRA:
Let the number of girls = G
Let the number of boys = B
There are 364 first-grade students
G + B = 364
there are 26 more girls than boys
G = B+26
Substitute B+26 for G in
G + B = 364
B+26 + B = 364
2B + 26 = 364
2B = 338
B = 169 boys
Substitute 169 for B in
G = B+26
G = 169+26
G = 195 girls.
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Edwin