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100 people were surveyed about an upcoming election. Of those surveyed, 75 said that did not feel that voting in elections was important. If 1200 people were surveyed, how many people would you expect to say that voting was not important? (Hint: set up a proportion)

77. 100100 people were surveyed about an upcoming election. Of those surveyed, 7575 said that did not feel that voting in elections was important. If 12001200 people were surveyed, how many people would you expect to say that voting was not important? (Hint: set up a proportion)

Full solution

Q. 77. 100100 people were surveyed about an upcoming election. Of those surveyed, 7575 said that did not feel that voting in elections was important. If 12001200 people were surveyed, how many people would you expect to say that voting was not important? (Hint: set up a proportion)
  1. Set up proportion: Set up the proportion using the numbers from the survey. The ratio of people who think voting is not important to the total number of people surveyed is 7575 to 100100.
  2. Find expected number: Set up the proportion to find the expected number out of 12001200. So, it's like 75100=x1200\frac{75}{100} = \frac{x}{1200}, where xx is the number of people who would say voting is not important out of 12001200.
  3. Cross-multiply to solve: Cross-multiply to solve for xx. So, 75×1200=100×x75 \times 1200 = 100 \times x.
  4. Do the multiplication: Do the multiplication. 75×1200=9000075 \times 1200 = 90000.
  5. Divide to solve for x: Divide by 100100 to solve for xx. So, 90000/100=x90000 / 100 = x.
  6. Final result: Do the division. 90000/100=90090000 / 100 = 900. So, x=900x = 900.

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