Your method is excellent . . . and your answer is correct!
I'll show you a method I often use.
Amy plays one game of snooker and one game of billards each Friday.
The probability that she wins every Friday is as follows:
. . Snooker: Win = 1/3
. - Billards: Win = 3/4
If she plays one game of each for a number of Fridays,
calculate how many games Amy did not win at either
if she won at both on 21 Fridays.
The probability that Amy wins both games on a particular Friday is:
Since she won both games 21 times, we assume she played on 84 Fridays.
Place the information in a chart . . .
We know that she wins of her snooker games.
We know that she wins of her billiards games.
Enter that information in our chart:
Now you can supply the missiing numbers and answer the question.