1999 CEMC Gauss (Grade 8) Problems/Problem 19

Problem

In a traffic study, a survey of $50$ moving cars is done and it is found that $20\%$ of these contain more than one person. Of the cars containing only one person, $60\%$ of these are driven by women. Of the cars containing just one person, how many were driven by men?

$\text{ (A) }\ 10 \qquad\text{ (B) }\ 16 \qquad\text{ (C) }\ 20 \qquad\text{ (D) }\ 30 \qquad\text{ (E) }\ 40$

Solution 1

We can find the total number of people who drove with more than one person in the car, and subtract it from the total to find the number of people who drove with only one person in the car.

Since $20\%$ of people drove a car with more than one person, we have:

$20\% \times 50 = \frac{1}{5} \times 50 = 10$ people who drove a car with more than one person

Thus, $50 - 10 = 40$ people drove with only one person in the car.

Of these $40$ people, $60\%$ were women, so $40 \times 60\% = 40 \times \frac{6}{10} = 24$ of them were women.

The rest of them were men, so $40 - 24 = \boxed {\textbf {(B) } 16}$ were men.

~anabel.disher

Solution 2

We can also subtract the percentages from $100\%$ , and then use those percentages to find the number of people. Since $20\%$ of people drove a car with more than one person, the rest of them drove with only one person, which was $100\% - 20\% = 80\%$ of the people who drove a car.

$50 \times 80\% = 50 \times {8}{10} = 40$

Of these $40$ people, $60\%$ were women, so $100\% - 60\% = 40\%$ were men.

This means that there were $40 \times 40\% = 40 \times \frac{4}{10} = \boxed {\textbf {(B) } 16}$ men that drove with only one person in their cars.

~anabel.disher

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1999 CEMC Gauss (Grade 8) Problems/Problem 19

Problem

Solution 1

Solution 2