Knowing that there is a total of 250 6th grade students that participated in the challenge:
a. You can identify that:
-The percentage of students that participated in lifting leights is 8%.
A percent can be written as a decimal number by dividing it by 100:
![(8)/(100)=0.08](https://img.qammunity.org/2023/formulas/mathematics/college/hgw3h8fmq65pb0v9orlblnik7tq8y8nu17.png)
Therefore, the number of students that participated in that exercise is:
![(250)(0.08)=20](https://img.qammunity.org/2023/formulas/mathematics/college/m27fawqlohqoctl1qlr1ly4ecrcfjrh6q5.png)
- The percentage of students that participated in running is 30%.
Therefore, the number of them that participated in this exercise is:
![(250)((30)/(100))=75](https://img.qammunity.org/2023/formulas/mathematics/college/2yvyt1flzz2bbkwjqed2vfzr553v2q1hzf.png)
- Notice that the percentage of students that participated in swimming is 5%.
Hence, the number of them that participated in this exercise is:
![(250)((5)/(100))\approx13](https://img.qammunity.org/2023/formulas/mathematics/college/89cgsa8fcpo4jaclu092d0ajcsrgwuccuk.png)
b. Notice that the number of students who chose walking is:
![(250)((17)/(100))\approx43](https://img.qammunity.org/2023/formulas/mathematics/college/ypbvpphrdfnl5dg8a2fav9cwhxkg75mwq5.png)
Therefore, the total number of students that chose swimming, walking, and lifting weight is:
![13+43+20=76](https://img.qammunity.org/2023/formulas/mathematics/college/tltwq2xk1p3a5thx0uza1ew1x123xlxr0t.png)
Notice that that number is greater than the number of students who chose running.
Hence, the answers are:
a. Lifting Weights:
![20\text{ students}](https://img.qammunity.org/2023/formulas/mathematics/college/wf9rqm5csu89ir03v4a8imit5en699utj8.png)
Running:
![75\text{ students}](https://img.qammunity.org/2023/formulas/mathematics/college/43wu7rjgjxh0yzsfzzoumm662fmwyy9gjr.png)
Swimming:
![13\text{ students}](https://img.qammunity.org/2023/formulas/mathematics/college/hn1s4eclru2p4hz9jw0pfbvheo8lorgebk.png)
b. Joseph is right, because there are 76 students who chose swimming, walking, and lifting weights, and there are 75 students who chose running.