SOLUTION: There are 364 first-grade students. If there are 26 more girls than boys, how many girls are there?

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Question 898793: There are 364 first-grade students. If there are 26 more girls than boys, how many girls are there?
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
b + (b+26) = 364
2b = 338
b = 169, number of boys. 338-169 girls

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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