Of 350 male athletes at a high school, some play only basketball, some play only baseball, and some do both. If 250 of the males play basketball, and 120 play both sports, how many of the males play baseball?
(1 point)
100
220
130
O 120
Let's use the principle of inclusion-exclusion to solve this problem.
We start by adding the number of males who play basketball (250) and the number of males who play baseball (x):
250 + x = Total number of males who play basketball or baseball
However, this sum includes the males who play both sports twice (they are counted in both the basketball and baseball categories), so we need to subtract the number of males who play both sports (120):
250 + x - 120 = Total number of males who play basketball or baseball, without counting duplicates
We know that the total number of male athletes at the high school is 350, so we can write:
250 + x - 120 = 350
Now, we can solve for x:
x = 350 - 250 + 120
x = 220
Therefore, 220 of the males play baseball.
The correct answer is 220.
To find out how many of the males play baseball, we need to subtract the number of males who play both sports (basketball and baseball) from the total number of males who play basketball.
Total number of males who play basketball = 250
Number of males who play both sports = 120
Number of males who play only basketball = Total number of males who play basketball - Number of males who play both sports
Number of males who play only basketball = 250 - 120
Number of males who play only basketball = 130
Since some males play only basketball and some play both sports, the remaining males must play baseball.
Therefore, the number of males who play baseball = 350 - (Number of males who play only basketball + Number of males who play both sports)
Number of males who play baseball = 350 - (130 + 120)
Number of males who play baseball = 350 - 250
Number of males who play baseball = 100
Therefore, 100 of the males play baseball.
To find out how many of the males play baseball, we can use the concept of sets and Venn diagrams. Let's break down the information given:
- The total number of male athletes at the high school is 350.
- 250 males play basketball, and 120 males play both basketball and baseball.
First, we know that the total number of males who play basketball includes those who play only basketball and those who play both sports. So, we can subtract the males who play both sports from the total number of males who play basketball:
Total males who play only basketball = Total males who play basketball - Males who play both sports
Total males who play only basketball = 250 - 120
Total males who play only basketball = 130
Now, we know that the total number of males who play basketball or baseball includes those who play only basketball, those who play only baseball, and those who play both sports. Since we know the total number of males who play basketball, we can subtract that from the total number of males:
Total males who play basketball or baseball = Total males - Total males who play only basketball
Total males who play basketball or baseball = 350 - 130
Total males who play basketball or baseball = 220
Therefore, the answer is 220. 220 of the males play baseball.