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.

Question

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 two-thirds.

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).

Ann · Answer

red-blue-purple = 4-3-2. red =160; blue = 120; purple -= 80.
New total 560. Red has increased from 160 to (add 75% = 120) 280. Extra blue is 200 - 120 = 80. Total blue = 120 + 80 = 200.
Blue as percentage of red = (200/280)x100 = 71.4%

Anonymous · Answer

Ali has 40 red buttons,60 green buttons,and 5 blue buttons