210 college students were asked in a survey if they preferred Windows or Mac brand computers. 85 students claimed that they preferred Mac to Windows brand computers. One fourth as many of the students who preferred Windows to Mac had no preference. How many of the students in the survey preferred Windows to Mac brand computers? A. 25 B. 50 C. 75 D. 100 E. 125

(D) The survey divides these college students into 3 groups, that do NOT overlap: preferred Mac to Windows, preferred Windows to Mac, had no preference. So the sum of numbers of students in these groups equals 210. Let’s denote the number of students who had no preference by x. Then the number of students who preferred Windows to Mac was 4x. 85 + 4x + x = 210 5x = 125 x = 25 The number of the students in the survey who preferred Windows to Mac brand computers was 4x = 4 × 25 = 100. The correct answer is D. ---------- It is confusing when it says the students had no prefernce. It is not sure if they liked netiher brand, or liked both.

It is confusing when it says the students had no preference. It is not sure if they liked neither brand, or liked both.

This question is about preference. They were asked which one they preferred. Like in a comparison, one of the choices could be more preferable (">" or "<"). Also, a student could have no preference ("="). In other words, it did not matter whether a student liked them both equally, or didn't like them both equally - he would still have no preference.

When a student found one of them more preferable, he still could be liking (or not liking) them both, but one of them more, than the other.

Could it be possible to do the same equation but saying that x is the number of students that preferred Windows to MAC and 1/4 of (x) are the students that had no preference?

Could it be possible to do the same equation but saying that x is the number of students that preferred Windows to MAC and 1/4 of (x) are the students that had no preference?

Yes, you can denote any unknown value by a variable. It is up to you to choose which one.

In your denotation the equation will be the following:

85 + x + x/4 = 210 5x/4 = 125 x = (125 / 5) × 4 x = 100

As you see we get the same answer to the question.

Note, that denoting the smallest value by a variable often helps to avoid fractions in an equation.

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