SOLUTION: There are 22 students in a music class in a school. Students in the class are either Freshmen or Sophomore, and there are 6 more boys than girls. If there are 5 Freshmen boys and 4

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Question 1201990: There are 22 students in a music class in a school. Students in the class are either Freshmen or Sophomore, and there are 6 more boys than girls. If there are 5 Freshmen boys and 4 Sophomore girls, how many Sophomores are in the class?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 13 sophomores


Explanation:

b = number of sophomore boys
b+5 = total number of boys since there are 5 freshmen boys.

There are 6 more boys, compared to girls
number of boys = (number of girls) + 6
number of girls = (number of boys) - 6
number of girls = (b+5) - 6
number of girls = b - 1


Since there are b-1 total girls and 4 sophomore girls, there must be (b-1)-4 = b-5 freshmen girls.

There are 5 freshmen boys and b-5 freshmen girls, so there are 5+(b-5) = b number of freshmen.

There are b sophomore boys and 4 sophomore girls, giving b+4 sophomores total.

Here's a table organizing the data so far.
BoysGirlsTotal
Freshmen5b-5b
Sophomoresb4b+4
Totalb+5 b-122

Add along the "total" row or column to get 2b+4 = 22 which solves to b = 9.

Then we can update the table into this
BoysGirlsTotal
Freshmen549
Sophomores9413
Total14822
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.
There are 22 students in a music class in a school.
Students in the class are either Freshmen or Sophomore, and there are 6 more boys than girls.
If there are 5 Freshmen boys and 4 Sophomore girls, how many Sophomores are in the class?
~~~~~~~~~~~~~~~


It can be solved in three simple steps. 


             Step 1 - determine how many boys are in the class


Let "b" be the number of boys in the class. 
Then the number of girls is (b-6).


The total students equation is

    b + (b-6) = 22,

which gives

    2b = 22 + 6,  2b = 28,  b = 28/2 = 14.  So, there are 14 boys in the class, in all.



             Step 2 - determine how many boys are the Sophomores


From total 14 boys, subtract 5 Freshmen boys and get 14-5 = 9 Sophomores boys.
   


             Step 3 - determine how many Sophomores are in the class


Add 4 Sophomore girls and 9 Sophomores boys to get 4+9 = 13 Sophomores in the class, in total.


ANSWER.  There are 13 Sophomores in the class, in all.

Solved.



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