Joshua surveys his friends to find out which recreational sport is most liked. He asks each of his friends if they prefer basketball, soccer, baseball, or volleyball. He finds 1/5 of his friends like volleyball and 2/5 prefer soccer. How many of Joshua’s friends prefer volleyball and soccer over the other two sports? (1 point)
To find out how many of Joshua's friends prefer volleyball and soccer over the other two sports, we need to subtract the number of friends who like basketball and baseball from the total number of friends.
From the information given, we know that 1/5 of Joshua's friends like volleyball and 2/5 prefer soccer. Therefore, the total proportion of friends who like volleyball and soccer is 1/5 + 2/5 = 3/5.
This means that 3/5 of Joshua's friends prefer volleyball and soccer over the other two sports.
So, if we let the total number of friends be x, then the number of friends who prefer volleyball and soccer would be (3/5) * x.
Therefore, the answer is (3/5) * x.
To find out how many of Joshua's friends prefer volleyball and soccer, we need to determine the fraction of friends who like each of the remaining two sports, basketball and baseball.
Here's how to do it:
1. Start with the information given: 1/5 of Joshua's friends like volleyball and 2/5 prefer soccer.
2. Determine the fraction of friends who like basketball. Since all the possible sports options have been mentioned, the fraction of friends who like basketball can be found by subtracting the fractions of friends who like volleyball and soccer from 1 (since the sum of the fractions should equal the whole).
So, the fraction of friends who like basketball is:
1 - (1/5 + 2/5) = 1 - 3/5 = 2/5.
3. Determine the fraction of friends who like baseball. Following the same logic as above, since basketball, volleyball, and soccer have been accounted for, the fraction of friends who like baseball can be found by subtracting the fractions of friends who like the other three sports from 1.
So, the fraction of friends who like baseball is:
1 - (1/5 + 2/5 + 2/5) = 1 - 5/5 = 0/5 = 0.
4. Finally, calculate how many of Joshua's friends prefer volleyball and soccer. Since 1/5 prefer volleyball and 2/5 prefer soccer, we can multiply these fractions to get the fraction of friends who like both sports:
(1/5) * (2/5) = 2/25.
Therefore, 2/25 of Joshua's friends prefer volleyball and soccer over the other two sports.
If 1/5 of Joshua’s friends like volleyball, then Joshua has 5*1/5 = <<5*1/5=1>>1 friend who likes volleyball.
If 2/5 of Joshua’s friends prefer soccer, then Joshua has 5*2/5 = <<5*2/5=2>>2 friends who prefer soccer.
The total number of friends who prefer volleyball or soccer is 1+2 = <<1+2=3>>3. Answer: \boxed{3}.