Question

Gary has guitar lessons every 5 days and band practice

every 4 days. His first band practice is in 4 days and his
first guitar lesson is in 5 days. In 100 days, how many
times will Gary have had guitar lessons and band
practice on the same day? Explain how you know.

Answer 1

Step-by-step explanation:

gary would have had 20 guitar practices. and 23 band practices. because if you count by fours all the way up to one hundred you add 1 every-time you add four and in the end it adds up to be 23. same with the guitar practices every five you add one and then it adds up to 20.

Answer 2

Answer: He will have guitar lessons and band practice at the same day 5 times.

Step-by-step explanation:

Hi, to answer this question we have to find the least common multiple (LCM) of both numbers:

5 : 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100

4: 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100

So, the LCM is 20, it means that every 20 days he will have practice and lessons the same day.

If we divide 100 /200 = 5

He will have guitar lessons and band practice at the same day 5 times.

Feel free to ask for more if needed or if you did not understand something.