Anthony has been saving nickels dimes quarters over the last year he knows that he has twice as many nickels as quarters. changes the coins to the change machine to exchange then for paper money. He learns that he has 260 coins totaling 29.75. The number of each type of coin Anthony saved. Fill in the blanks

Answer:The number of nickel's coin is 150The number of dime's coin is 35The number of quarter's coin is 75Step-by-step explanation:Letx ----> the number of nickel's coiny ---> the number of dime's coinz ---> the number of quarter's coinRemember that[tex]1\ nickel=\$0.05[/tex][tex]1\ dime=\$0.10[/tex][tex]1\ quarter=\$0.25[/tex]we know that[tex]x+y+z=260[/tex] ----> equation A[tex]0.05x+0.10y+0.25z=29.75[/tex] ----> equation B[tex]x=2z[/tex] ----> equation Csubstitute equation C in equation A and equation B[tex]2z+y+z=260[/tex] [tex]3z+y=260[/tex] ---> equation A1[tex]0.05(2z)+0.10y+0.25z=29.75[/tex][tex]0.35z+0.10y=29.75[/tex] -----> equation B1Solve the system of equations A1 and B1 by graphingRemember that the solution is the intersection point both graphsThe solution is the point (75,35)see the attached figuresoz=75, y=35Find the value of x[tex]x=2(75)=150[/tex]thereforeThe number of nickel's coin is 150The number of dime's coin is 35The number of quarter's coin is 75