How are dancers self-taught?

The Sunnyville School 5th graders were doing a play. There was a big dance scene with dancers in rows.?

• Use these hints to figure out how many dancers there were. There were 40 fifth graders but not all of them danced. When the dancers rehearsed in rows of 2, one dancer was left to dance alone When the dancers rehearsed in rows of 3, 2 dancers were left to dance together. When the dancers rehearsed in rows of 4, 3 dancers were left to dance together. When the dancers rehearsed in rows of 5, finally every dancer was in a row. How many dancers danced? EXPLAIN YOUR ANSWER.

• Answer:

  Let D = # of dancers There were 40 fifth graders but not all of them danced. So D < 40 When the dancers rehearsed in rows of 2, one dancer was left to dance alone So if you divide the group into rows with two dancers in each row, then you'll have one dancer left over. Expressing it mathematically, D / 2 has a remainder of 1 When the dancers rehearsed in rows of 3, 2 dancers were left to dance together. D / 3 has a remainder of 2 When the dancers rehearsed in rows of 4, 3 dancers were left to dance together. D / 4 has a remainder of 3. Also, you know you have to have at least seven dancers, because the minimum number you need to have with one row of four dancers and three left over is 7. When the dancers rehearsed in rows of 5, finally every dancer was in a row. D / 5 has a remainder of 0, therefore the number of dancers has to be a multiple of 5, either: 10, 15, 20, 25, 30, or 35 So, just take each of these numbers and divide them each by 2, 3, and 4, and see what the remainders are. They should match the remainders above. Let's look at 10: 10 / 2 = 5 with no left over, so it can't be 10. In fact, it can't be any even number because dividing an even number by 2 will always leave you with none left over. So now your possible choices are: 15, 25, or 35 15 / 2 = 7, with a remainder of 1 15 / 3 = 5, with no remainder, so you know it's not 15 25 / 2 = 12 with a remainder of 1 25 / 3 = 8 with a remainder of 1, so it's not 25 35 / 2 = 17 with a remainder of 1 35 / 3 = 11 with a remainder of 2 35 / 4 = 8 with a remainder of 3 So the answer is 35 dancers.