Answered

2. In the March 1998 issue of Great Goatee Magazine, readers could vote online for their
favorite goatee in the Pitt-Brust Bonanza. Readers could either vote for Brad Pitt or Mr. Brust. Brust's
votes equaled 2 times the sum of Pitt's votes and 400. The total number of votes received was 2012.
Model the situation with a linear system.
a.
Pitt?
Total # of votes:
Brust vs Pitt:
Let B # vote for Brust
Let P=#votes for Pitt
= 2(.
= 2012
LON BY SHged Fa
Brust?



Answer :

mhanifa

Brust's votes equaled 2 times the sum of Pitt's votes and 400:

  • B = 2(P + 400), this is the first equation

The total number of votes received was 2012:

  • B + P = 2012, this is the second equation

Solve for P by substitution:

  • 2(P + 400) + P = 2012
  • 2P + 800 + P = 2012
  • 2P = 2012 - 800
  • 2P = 1212
  • P = 606

Find B:

  • B =2012 - 606
  • B = 1406
semsee45

Answer:

a)   Total # of votes:   B + P = 2012

     Brust vs Pitt:   B = 2(P + 400)

b)   1608 = votes for Brust

      404 = votes for Pitt

      Brust won by 1204 votes

Step-by-step explanation:

Given variables:

  • Let B = the number of votes for Brust
  • Let P = the number of votes for Pitt

Given information:

  • Brust's votes equalled 2 times the sum of Pitt's votes and 400.
  • The total number of votes received was 2012.

Create a system of linear equations using the given variable and information:

  • Total # of votes:   B + P = 2012
  • Brust vs Pitt:   B = 2(P + 400)

Substitute the second equation into the first equation and solve for P:

⇒ 2(P + 400) + P = 2012

⇒ 2P + 800 = 2012

⇒ 3P = 1212

⇒ P = 404

Substitute the found value of P into the first equation and solve for B:

⇒ B + 404 = 2012

⇒ B = 1608

Therefore:

  • 1608 = votes for Brust
  • 404 = votes for Pitt

To find how many votes Brust won by, subtract the total number of votes for Pitt from the total votes for Brust:

⇒ 1608 - 404 = 1204

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