math
posted by Dell .
Marnie collects red, blue and purple buttons. At the beginning of the year she has 360 buttons in a box. The ratio of red buttons to blue buttons is 4:3 and there are twice as many red buttons as purple buttons.
a.What is the ratio of blue buttons to purple buttons at the beginning of the year?
b.After Marnie adds another 200 buttons –some red and some blue – at the end of the year, the number of red buttons increased by 75% and the number of blue buttons increased by twothirds.
i.What is the new ratio of red buttons to blue buttons?
ii.Express the number of purple buttons as a fraction of the new total number of buttons.
iii.Express the number of blue buttons as a percentage of the number of red buttons. (Round to one decimal place).

so, we have red:blue:purple = 4:3:2
4+3+2=9, so there are 360/9 buttone for each proportion:
160 red
120 blue
80 purple
b:p = 3:2
after new buttons, we have
red: 160 (1.75) = 280
blue: 120(5/3) = 200
purple: 80
r:b = 280:200 = 7:5
p/all = 80/560 = 1/7
b/r = 200/280 = 5/7 = 71.4% 
I'm confused on where you got the 1.75 and the 5/3????