Question

6

Answer 1

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

$B = 325$

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