there are 1700 seats in a theatre. 40% of the tickets to a concert at the theatre are category 1 tickets and the rest are of other categories. The organizer decides to change some tickets from the other categories to category 1. The number of tickets of other categories then become 55%. How many more category 1 tickets are added?

255 added

Step-by-step explanation:

1700 x 55% = 935

1700 x 40% = 680

935 - 680 = 255

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: