Final answer:
Rafael won 21 times out of the 30 tennis matches played against Roger, based on the ratio of their wins being 7:3.
Step-by-step explanation:
The question asks us to calculate the number of times Rafael won in a series of tennis matches against Roger, given the ratio of Rafael's wins to Roger's wins is 7:3 and the total matches played were 30. Since the ratio represents parts of the whole, we can define '7x' as the number of wins for Rafael and '3x' for Roger. Combining these wins, we have that 7x + 3x equals the total number of matches, thus, 10x = 30.
To find the value of 'x', we divide both sides of the equation by 10 which gives us: x = 30 / 10, so x = 3. Now that we know the value of 'x', we can work out the number of times Rafael won by plugging 'x' back into '7x':
Rafael's wins = 7x = 7 * 3 = 21.