Question

Don't spam.
Wrong answer will be reported ​

Answer 1

QUESTION:

If n(U) = 125, y is two times of x and z is 10 more than x. Then find the vaues of x, y and z

ANSWER:

x = 21.25

y = 42.5

z = 31.25

GIVEN:

y = 2x

z = x + 10

TO FIND:

The vaues of x, y and z.

FORMULA:

$n(x \: \: \cup \: \: y \: \: \cup \: \: z) = n(x) + n(y) + n(z) \\ - n(x \: \: \cap \: \: y) - n(x \: \: \cap \: \: z) - n(y \: \: \cap \: \: z) \\ + n(x \: \: \cap \: \: y \: \: \cap \: \: z)$

EXPLANATION:

n(X) = x + 4 + 3 + 6

n(Y) = y + 4 + 3 + 17

n(Z) = z + 6 + 3 + 17

n(X ⋂ Y) = 4 + 3

n( X ⋂ Z) = 6 + 3

n(Y ⋂ Z) = 17 + 3

n(X ⋂ Y ⋂ Z) = 3

Substitute these values in the equation

125 = x + 4 + 3 + 6 + y + 4 + 3 + 17 + z + 6 + 3 + 17 - (4 + 3) - (6 + 3) - (17 + 3) + 3

Substitute y = 2x and z = x + 10

125 = x + 13 + 2x + 24 + x + 10 + 26 - 7 - 9 - 20 + 3

125 = 4x + 76 - 36

125 = 4x + 40

125 - 40 = 4x

4x = 85

x = 21.25

y = 2x = 42.5

z = x + 10 = 31.25

Answer 2

:

n(U) = 125, y is two times of x and z is 10 more than x. Then find the vaues of x, y and z

ANSWER:

x = 21.25

y = 42.5

z = 31.25

GIVEN:

y = 2x

z = x + 10

TO FIND:

The vaues of x, y and z.

FORMULA:

EXPLANATION:

n(X) = x + 4 + 3 + 6

n(Y) = y + 4 + 3 + 17

n(Z) = z + 6 + 3 + 17

n(X ⋂ Y) = 4 + 3

n( X ⋂ Z) = 6 + 3

n(Y ⋂ Z) = 17 + 3

n(X ⋂ Y ⋂ Z) = 3

Substitute these values in the equation

125 = x + 4 + 3 + 6 + y + 4 + 3 + 17 + z + 6 + 3 + 17 - (4 + 3) - (6 + 3) - (17 + 3) + 3

Substitute y = 2x and z = x + 10

125 = x + 13 + 2x + 24 + x + 10 + 26 - 7 - 9 - 20 + 3

125 = 4x + 76 - 36

125 = 4x + 40

125 - 40 = 4x

4x = 85

x = 21.25

y = 2x = 42.5

z = x + 10 = 31.25

Pl inbox me