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Marta_Voda [28]
4 years ago
9

Peter has twice as many stickers as Joe. Joe has 40 more stickers than Emily. They have 300 Stickers altogether. How many sticke

rs does Peter have?
Mathematics
1 answer:
GarryVolchara [31]4 years ago
4 0

Answer:

170

Step-by-step explanation:

Equations derived from given info.

  • P=2J
  • J=E+40
  • P+J+E=300

Use some substitution now.

  • P=2(E+40)
  • J=E+40
  • P+J+E=300

Substitute first and second equation into third.

  • 2(E+40)+E+40+E=300
  • 2E+80+E+40+E=300
  • 4E+120=300
  • 4E=180
  • E=45

Emily has 45 stickers. But we want to know what Peter has.

Use P=2(E+40)

  • P=2(45+40)
  • P=90+80
  • P=170

Peter has 170 stickers.

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8/x-5 - 9/x-4 = 5/x^2-9x+20
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If you're using the app, try seeing this answer through your browser:  brainly.com/question/2752942

_______________


Solve the equation:

\mathsf{\dfrac{8}{x-5}-\dfrac{9}{x-4}=\dfrac{5}{x^2-9x+20}\qquad\qquad(x\ne 5~and~x\ne 4)}


Reduce the fractions at the left side so that they have the same denominator:

\mathsf{\dfrac{8(x-4)}{(x-5)(x-4)}-\dfrac{9(x-5)}{(x-4)(x-5)}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32}{x^2-4x-5x+20}-\dfrac{9x-45}{x^2-4x-5x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32}{x^2-9x+20}-\dfrac{9x-45}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32-(9x-45)}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}


Numerators must be equal:

\mathsf{8x-32-(9x-45)=5}\\\\
\mathsf{8x-32-9x+45=5}\\\\
\mathsf{8x-9x=5+32-45}\\\\
\mathsf{-x=-8}\\\\
\mathsf{x=8}\quad\longleftarrow\quad\textsf{this is the solution.}


I hope this helps. =)


Tags:  <em>rational equation fraction solution algebra</em>

7 0
3 years ago
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