Theoretical probability is expressed as
Number of favourable outcomes/number of total outcomes
Let x represent the total number of tiles in the bag
Let v represent the number of tiles that are vowels
If there are 63 consonant tiles, then
v + 63 = x
We were told that the theoretical probability of choosing a vowel is 30%. Expressed in decimal,
it is 30/100 = 0.3
This also means that
v/x = 0.3
Substituting x = v + 63 into v/x = 0.3, we have
v/(v + 63) = 0.3
By crossmultiplying,
v = 0.3(v + 63)
v = 0.3v + 18.9
v - 0.3v = 18.9
0.7v = 18.9
v = 18.9/0.7
v = 27
x = 63 + 27 = 90
There are 90 tiles in the bag