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How Do You Solve a Word Problem Using a Percent Proportion?

In a recent survey 80% of people polled said algebra was their favorite subject. If 68 people gave this answer how many were polled?

Summary

  1. 'n' is a variable that represents the total number of people polled
  2. Set up a percent proportion
  3. 80 over 100 on the left, and 68 over 'n' on the right
  4. Cross multiply to solve for 'n'
  5. 80 times 'n' is on the left, and 100 times 68 on the right
  6. Divide both sides by 80
  7. 85 people were polled

Notes

    1. 'n' is a variable that represents the total number of people polled
    1. '%' stands for percent
    1. The term 'part' refers to 'part of the whole', or a portion of a total
    2. In our problem 68 is the 'part'
    1. We need to find the percent, part, and the whole
    1. The left hand side is 80 over 100
    1. 68 is the part of the total number of people polled
    1. 68 is the part of the total number of people polled, which is the numerator on the right
    1. 'n' is a variable that represents the total number of people polled
    1. 'n' is a variable that represents the total number of people polled
    2. Cross multiplication is when we multiply the numerators of fractions by the opposite denominators
    1. 'n' is a variable that represents the total number of people polled
    2. Multiply the first numerator by the second denominator
    1. Multiply the first denominator by the second numerator
    1. Multiply 68 by 100
    2. 68 • 100 = 6800
    1. Divide both sides by 80 to solve for 'n'
    2. 'n' is a variable that represents the total number of people polled
    3. The 80's cancel out on the left
    4. 6800 divided by 80 is 85 on the right
    1. 'n' is a variable that represents the total number of people polled