In a maths tutorial, some of the students did maths games and the rest of the students did problem solving. The students doing maths games worked in groups of 3 The students doing problem solving worked in groups of 5 There were 7 groups altogether. How many students were at the tutorial?
Question
In a maths tutorial, some of the students did maths games and the rest of the students did problem solving.
The students doing maths games worked in groups of 3 The students doing problem solving worked in groups of 5 There were 7 groups altogether. How many students were at the tutorial?
Solution
To solve this problem, we need to consider the possible combinations of groups that add up to 7.
Step 1: Consider the possible combinations of groups
- The number of groups of 3 (maths games) could be 1, 2, or 3.
- The number of groups of 5 (problem solving) could be 1, or 2.
Step 2: Find a combination that adds up to 7
- If there were 1 group of 3 and 2 groups of 5, that would add up to 3 groups, not 7.
- If there were 2 groups of 3 and 1 group of 5, that would add up to 3 groups, not 7.
- If there were 2 groups of 3 and 2 groups of 5, that would add up to 4 groups, not 7.
- If there were 3 groups of 3 and 1 group of 5, that would add up to 4 groups, not 7.
The only combination that adds up to 7 groups is 2 groups of 3 (maths games) and 5 groups of 5 (problem solving).
Step 3: Calculate the total number of students
- 2 groups of 3 students = 6 students
- 5 groups of 5 students = 25 students
So, there were 6 + 25 = 31 students at the tutorial.
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