Question

6

PO
2. In school of 900 studonts, it was
found that 600 students participate
in singing 500 students
in dancing and 125
do not participate
in both the activities.
participate​

Answer 1

`B = 325`

Explanation:

Given

Total = 900

Singing = 600

Dancing = 500

None = 125

Required

Determine the number of students that participate in both

Representing; Singing with S, Dancing with D, Both singing and dancing with B and None with N;

In Set Notation;

`Total = (S - B) + (D - B) + N + B`

Substitute 900 for Total, 600 for S, 500 for D and 125 for N

`900 = (600 - B) + (500 - B) + 125`

Open Brackets

`900 = 600 - B + 500 - B + 125 + B`

Collect Like Terms

`900 = 600 + 500 + 125 - B - B + B`

`900 = 1225- B - B + B`

`900 = 1225- B`

Collect Like Terms

`900 - 1225 = -B`

`-325 = -B`

Multiply both sides by -1

`-1 * -325 = -B * -1`

`325 = B`

Reorder

`B = 325`

Hence, the number of students that do not participate in both is 325