A band played 20 songs. They took 3 breaks. After the last break they played 3 songs. They played twice as many songs after the previous break. They played 5 songs before their first break. How many songs did they play between their first break and their second break?

The band played 6 songs between their first break and second break.

Step-by-step explanation:

Step 1; First we divide the total time they played. They took 3 breaks. So they played 4 times with 3 breaks in between. They played the first time, took their first break, played the second time, took their second break, played their third time, took their third break and then played a final fourth time.

Step 2; It is given that the band played 3 songs after their last break. They played twice as many songs after their previous break. The last sentence means they played twice as many songs that they played after the third break after the second break. This means they played 3 * 2 songs after the second break, they played 6 songs after the second break. So in these two playtimes, they played 3 + 6 songs, 9 songs in total. It also says they played 5 songs before their first break. So in three playtimes, they played 5 + 9 = 14 songs. One before their first break, 6 before their last break and 3 after their last break.

Step 3; So in total, the band played 14 songs. They played a total of 20 songs. So they played the remaining songs in between their first and second breaks.

Songs played between the first and second breaks = 20 - 14 = 6 songs.