Respuesta :

SaniShahbaz

Answer:

  • The number of nickels = [tex]x[/tex] = 15
  • The number of dimes = [tex]y[/tex] = 12

Step-by-step explanation:

  • Let x be the number of nickels
  • Let y be the number of nickels

As

Jocelyn has $1.95 in her pocket made up of 27 nickels and dimes.

So, the equation becomes

[tex]x\:+\:y\:=\:27....[A][/tex]    

[tex].05x + .10y = 1.95[/tex]

Multiplying both sides by 20

[tex]x\:+\:2y\:=\:39[/tex]

[tex]x\:=\:39\:-2y[/tex]

Putting [tex]x\:=\:39\:-2y[/tex] in equation [A]

[tex]x\:+\:y\:=\:27[/tex]

[tex]\left(39\:-\:2y\right)\:+\:y\:=\:27[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]

[tex]39-2y+y=27[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:-2y+y=-y[/tex]

[tex]39-y=27[/tex]

[tex]\mathrm{Subtract\:}39\mathrm{\:from\:both\:sides}[/tex]

[tex]39-y-39=27-39[/tex]

[tex]-y=-12[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-y}{-1}=\frac{-12}{-1}[/tex]

[tex]y=12[/tex]

Putting [tex]y=12[/tex] in in equation [A]

[tex]x\:+\:y\:=\:27[/tex]

[tex]x\:+\:12\:=\:27[/tex]

[tex]\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}[/tex]

[tex]x+12-12=27-12[/tex]

[tex]x=15[/tex]

Therefore,

  • The number of nickels = [tex]x[/tex] = 15
  • The number of dimes = [tex]y[/tex] = 12

Keywords:  word problem

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