Section E Section E Checkpoint

Problem 1

In a class, the ratio of students who wear glasses to those who don’t is 3 to 5. If there are 32 students in the class, how many students wear glasses? Show your reasoning.

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Solution

12 students. Sample reasoning: The total number of parts in the ratio is 8. 32÷8=432 \div 8 = 4, so each part represents 4 students, and 3⋅4=123 \boldcdot 4 = 12.

Show Sample Response
Sample Response

12 students. Sample reasoning: The total number of parts in the ratio is 8. 32÷8=432 \div 8 = 4, so each part represents 4 students, and 3⋅4=123 \boldcdot 4 = 12.

Problem 2

In a school, the ratio of teachers who wear glasses to those who don’t is 7 to 2.

  1. If there are 10 teachers who don’t wear glasses, how many total teachers are at the school?
  2. Explain why you chose the strategy you did to solve the problem.
Show Solution
Solution

  1. 45 teachers. Sample reasoning:

  2. Sample response: With a tape diagram I can see the parts in the ratio (7 and 2) and the total number of parts (9). If the 2 parts for teachers who don’t wear glasses represent 10 teachers, each part represents 5 teachers and 9 parts represent 9⋅59 \boldcdot 5 or 45 teachers.
Show Sample Response
Sample Response

  1. 45 teachers. Sample reasoning:

  2. Sample response: With a tape diagram I can see the parts in the ratio (7 and 2) and the total number of parts (9). If the 2 parts for teachers who don’t wear glasses represent 10 teachers, each part represents 5 teachers and 9 parts represent 9⋅59 \boldcdot 5 or 45 teachers.