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almond37 [142]
3 years ago
7

6

Mathematics
1 answer:
denis23 [38]3 years ago
4 0

Answer:

B = 325

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;

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

<em>Hence, the number of students that do not participate in both is 325</em>

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