Answer:
The total number of flowers is 680
Step-by-step explanation:
Let
x -----> the number of flowers green
y ----> the number of flowers yellow
z ----> the number of flowers purple
we know that
[tex]x=\frac{3}{10}(x+y+z)[/tex] ----> equation A
The 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 C
Remember 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 x
substitute in the equation A
[tex]x=\frac{3}{10}(680)=204[/tex]
Find the value of y
substitute in the equation B
[tex]y=\frac{21}{40}(680)=357[/tex]
therefore
The number of flowers green is 204
The number of flowers yellow is 357
The he number of flowers purple is 119
The total number of flowers is 680
