Hannah and Francine have $120. Hannah and Peter have $230. Peter has six times as much as Francine. How much does Hannah have?

Answer:The amount that Hannah has is $98Step-by-step explanation:Letx-----> amount that Hannah hasy ----> amount that Francine hasz ----> amount that Peter haswe know that[tex]x+y=120[/tex] ----> equation A[tex]x+z=230[/tex] ----> equation B[tex]z=6y[/tex] -----> equation Csubstitute equation C in equation B[tex]x+6y=230[/tex] ----> equation Dwe have[tex]x+y=120[/tex] ----> equation A[tex]x+6y=230[/tex] ----> equation DSolve the system of equations A and D by graphingRemember that the solution is the intersection point both graphsusing a graphing toolThe solution is the point (98,22)see the attached figureFind the value of z[tex]z=6y[/tex] ----> [tex]z=6(22)=132[/tex]thereforeThe amount that Hannah has is $98The amount that Francine has is $22The amount that Peter has is $132