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.
| Boys | Girls | Total | | Freshmen | 5 | b-5 | b | | Sophomores | b | 4 | b+4 | | Total | b+5 | b-1 | 22 |
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
| Boys | Girls | Total | | Freshmen | 5 | 4 | 9 | | Sophomores | 9 | 4 | 13 | | Total | 14 | 8 | 22 |
Answer by ikleyn(52856)  (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?
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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.
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