Question 1202097: There are 22 students in a music class in a school. The students in the class are either Freshmen or Sophomores, 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 ikleyn, Theo:
Answer by ikleyn(52884)   (Show Source):
You can put this solution on YOUR website! .
I just solved this problem at this forum a week ago. See the link
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1201990.html
For your convenience, I place this my solution here again:
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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.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! i get 13 sophomores.
you are given that there are 22 students total.
you are given that there are 6 more boys than girls.
you are given that there are freshmen boys and 4 sophomore girls.
let b = number of boys and g = number of girls.
you get b + g = 22
since b = g + 6, you get g + 6 + g = 22.
combine like terms to get 2g + 6 = 22
subtract 6 from both sides of the equation to get 2g = 16
solve for g to get g = 8.
since b = g + 6, then b = 14
since 5 boys are freshmen, then 9 boys must be sophomores.
since 4 girls are sophomores, then 4 girls must be freshmen.
the freshman class has 5 boys and 4 girls = 9 total.
the sophomore class has 9 boys and 4 girls = 13 total.
the number of sophomores in the class is equal to 13.
i made a chart that you see below:
freshmen sophomores total
boys 5 9 14
girls 4 4 8
total 9 13 22
looks good to me.
hopefully you agree.
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