Final answer:
Therefore, TJ has 18 rock songs on his favorite playlist.
Step-by-step explanation:
To find out how many rock songs TJ has, we first need to calculate the total number of songs that are not pop, rap, or country. Since 1/3 of the songs are pop, 1/6 are rap, and 1/8 are country, we can add these fractions together: 1/3 + 1/6 + 1/8. To add these fractions, we need a common denominator, which is 24. So, 1/3 is equivalent to 8/24, 1/6 is equivalent to 4/24, and 1/8 is equivalent to 3/24. Adding these fractions, 8/24 + 4/24 + 3/24 gives us 15/24.
Since 15/24 represents the songs that are not pop, rap, or country, we can subtract this fraction from the total number of songs to find the number of rock songs. TJ has 48 songs in total, so 15/24 of those songs are not rock. By subtracting 15/24 from 48, we get: 48 - (15/24 x 48) = 48 - (15/24) x 48 = 48 - 15 x 2 = 48 - 30 = 18.
Therefore, TJ has 18 rock songs on his favorite playlist