school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers, with the same combination of sixth- and seventh-grade students in each group. She wants to form as many groups as possible.
A) What is the largest number of groups that could be formed? Just type the number.
B) If that many groups are formed, how many students of each grade level would be in each group?
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Answers
Given : A school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers, with the same combination of sixth- and seventh-grade students in each group. She wants to form as many groups as possible.
To Find :
A) What is the largest number of groups that could be formed? Just type the number.
B) If that many groups are formed, how many students of each grade level would be in each group?
Solution:
in 6th grade = 90
in 7th grade = 75
we need to find HCF of 90 and 75 to find maximum number of groups
90 = 2 * 3 * 3 * 5
75 = 3 * 5 * 5
3 is the only common factor
HCF = 3
3 Groups can be formed
largest number of groups that could be formed = 3
Students of 6th grade in a group = 90/3 = 30
Students of 7th grade in a group = 75/3 = 25
Total in a group = 30 + 25 = 55
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