Question

A bag contains counters that are red, blue, green or yellow. The number of counters are 9 which is red, 3x is blue, x-5 is green, 2x is yellow. A counter is chosen at random. The probability it is red is 9/100. Work out the probability it is green.

Answer 1

so as there are 9 reds, you know that the total number of counters is 100 (because red probability is 9/100)
so you can work out x by writing an equation.
9 + 3x + x - 5 + 2x = 100
from here you can add up all of the x's and the numbers (so you have 3x+x +2x = 6x)(and for numbers you have 9 and -5, 9 - 5 = 4) so putting these together you have 6x and 4 you get the following:
6x + 4 = 100
take away 4 from both sides
6x = 96
divide both sides by 6
x =96/6 = 16
green is x-5 so if you substitute the result we got for x...
16-5 = 11. so there are 11 greens
therefore the probability would be 11/100 as there are 100 counters overall.