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in a class of 28 students everyone like math, english, or both. if 17 like math and 19 like english how many like both?

A) 2
B) 8
C) 16
D) 20
E) 28

Respuesta :

mhanifa

Answer:

  • B) 8 students like both

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Let the numbers be:

  • M - likes math, M = 17;
  • E - likes English, E = 19;
  • B - likes both, B is unknown;
  • T- total number, T = 28.

Since both M and E include B, we can show the total as:

  • Math only + English only + Both = Total

and

  • Math only = M - B
  • English only = E - B

The total can be expressed as:

  • M - B + E - B + B = T
  • M + E - B = T

Substitute values and solve for B:

  • 17 + 19 - B = 28
  • 36 - B = 28
  • B = 36 - 28
  • B = 8

This is matching the answer choice B)

Maths be A and English be B

  • A+B-A[tex]\cap[/tex] B=AUB

A intersection B be X

  • (A-X)+(B-X)+X=AUB
  • A+B-X=28
  • 17+18-X=18
  • 35-X=28
  • X=8

Option B

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