A) In a classroom somewhere in the US, a teacher tells his students (half-joking

Question

A) In a classroom somewhere in the US, a teacher tells his students (half-jokingly) that "for every 2 of you who are enjoying this math lesson, there are 3 of you who are not enjoying it." Since they happened to be talking about ratio and proportion, a few students attempted to restate their teacher's "joke." For each student, determine if their statement is mathematically accurate. If so, explain/show why. If not, fix their statement so that it is accurate.

Oliver: That means that 2/3 of us are enjoying the lesson!

Jace: This means that 50% more students are not enjoying the lesson, as compared to those enjoying it!

B) Over the years, I've noticed that math 122 classes have approximately a 1:8 ratio of men to women. Suppose that during one odd semester, three-fourths of the men and one-half of the women in the class drop. If at the end of the Semester there are 15 more women than men in the class, how many men and how many women were in the class at the start of the semester AND how many were in the class at the end of the semester?

Explanation / Answer

a) for every 2 of you who are enjoying the math class there are 3 of you who are not enjying

this means that ratio that is enjoying is 2/5 and ratio that is not enjoying is 3/5

b) lets say no. of men = x and women = 8x

Total = 1x + 8x = 9x

3/ 4th of men = 3/4 (1x) = 3x / 4

1/2 (8x) = 4x

so 3x/4 and 4x drop

So, remaining men = x - 3x/4 = x/4

remaining women = 8x -4x = 4x

there are 15 more women than men in the class,

4x - x/4 = 15

15x/4 = 15 ; x = 4

Men = x= 4

Women = 8x = 32

Total intially = 36 students

At the end of semester total students = x/4 + 4x = 4/4 + 4*4 = 1+16 = 17

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