SOLUTION: Hello, I would like some help with this algebra problem: Valley Community college has 4000 students.Of these 1/8 are full time students.Of the full-time students,3/10 are in fav

Question 601058: Hello, I would like some help with this algebra problem:
Valley Community college has 4000 students.Of these 1/8 are full time students.Of the full-time students,3/10 are in favor of having a socccer team.Of the students that are not full time, 4/5 are in favor of having a soccer team.How many students in school are not in favor of having a soccer team?
Do I have to multiply and then substract? I am not sure. Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
1/8 are full time. So 1 - 1/8 = 7/8 are not full time

"Of the full-time students,3/10 are in favor of having a socccer team", which means that (1/8)*(3/10) = 3/80 of the total are full time and are in favor.

The fraction of those who are full time but are not in favor is: (1/8)*(1 - 3/10) = (1/8)*(7/10) = 7/80

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"Of the students that are not full time, 4/5 are in favor of having a soccer team" means that (7/8)*(4/5) = 28/40 = 7/10 of the total are not full time and are in favor.

So the fraction of the students who are not full time and not in favor is: (7/8)*(1 - 4/5) = (7/8)*(1/5) = 7/40

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From above, we found the fractions of those who are not in favor for full time and non-full time students. These fractions were: 7/80 and 7/40

Add up these fractions to get: 7/80 + 7/40 = 7/80 + 14/80 = 21/80

So the fraction of the total number of students that are not in favor is 21/80

We know that there are 4000 students. So multiply this by that last fraction:

4000*(21/80) = 84000/80 = 1050

So 1050 students are not in favor of having a soccer team.
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