If 3/10 of the flowers are green and 3/4 of the rest are yellow. And the rest are purple. How many flowers do you have if you have 119 purple flowers

Answer:The total number of flowers is 680Step-by-step explanation:Letx -----> the number of flowers greeny ----> the number of flowers yellowz ----> the number of flowers purplewe know that[tex]x=\frac{3}{10}(x+y+z)[/tex] ----> equation AThe rest is equal to[tex]\frac{7}{10}(x+y+z)[/tex] so[tex]y=(\frac{3}{4})\frac{7}{10}(x+y+z)[/tex] [tex]y=\frac{21}{40}(x+y+z)[/tex] -----> equation B[tex]z=(\frac{1}{4})\frac{7}{10}(x+y+z)[/tex] [tex]z=\frac{7}{40}(x+y+z)[/tex] -----> equation CRemember that[tex]z=119[/tex]substitute in equation C and solve for (x+y+z)(x+y+z) ----> is the total of flowers[tex]119=\frac{7}{40}(x+y+z)[/tex][tex](x+y+z)=119(40)/7[/tex][tex](x+y+z)=680[/tex]Find the value of xsubstitute in the equation A[tex]x=\frac{3}{10}(680)=204[/tex]Find the value of ysubstitute in the equation B[tex]y=\frac{21}{40}(680)=357[/tex]thereforeThe number of flowers green is 204The number of flowers yellow is 357The he number of flowers purple is 119The total number of flowers is 680