ashmitaugrakoti
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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​

Respuesta :

MrRoyal

Answer:

[tex]B = 325[/tex]

Step-by-step 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;

[tex]Total = (S - B) + (D - B) + N + B[/tex]

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

[tex]900 = (600 - B) + (500 - B) + 125[/tex]

Open Brackets

[tex]900 = 600 - B + 500 - B + 125 + B[/tex]

Collect Like Terms

[tex]900 = 600 + 500 + 125 - B - B + B[/tex]

[tex]900 = 1225- B - B + B[/tex]

[tex]900 = 1225- B[/tex]

Collect Like Terms

[tex]900 - 1225 = -B[/tex]

[tex]-325 = -B[/tex]

Multiply both sides by -1

[tex]-1 * -325 = -B * -1[/tex]

[tex]325 = B[/tex]

Reorder

[tex]B = 325[/tex]

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

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