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How Do You Use a Proportion to Find What Percent a Part is of a Whole?

68 is what percent of 85?

Summary

  1. '%' stands for percent
  2. In math, 'is' means 'equals'
  3. Since we don't know what the percent is, we'll call that 'x'
  4. In math, 'of' means multiplication
  5. In a percent proportion we put the percent over 100
  6. Then we set that equal to the part over the whole
  7. Here our part is 68 and our whole is 85, so we have 68/85
  8. We can cross multiply to solve for 'x'
  9. 68 is 80% of 85

Notes

    1. First we want to rewrite our problem using math symbols
    1. '68 is what percent of 85?'
    2. In math, 'is' means 'equals'
    3. 'What percent' is our unknown: 'x'
    4. 'of' means we multiply
    5. The equation ends up being 68 = x • 85
    1. Using a percent proportion is one way we can solve for 'x'
    1. In our problem, our 'x' variable represents the percent
    1. We can identify each piece in the percent proportion from our equation
    1. 'x' is the variable representing the percent
    1. 68 is a percent of 85, which means it's part of 85
    1. Since the 68 is coming out of 85, 85 is the 'whole'
    1. Remember, 'x' is the variable representing the percent
    2. 85 is the 'whole' in our percent proportion
    1. 68 is the 'part' in our percent proportion
    1. Now we can just simplify to find 'x', our percent!
    1. 'x' is the variable representing the percent
    1. 100•68 is 6800
    2. When we divide this by 85, we get 80
    1. 'x' is the variable representing the percent
    2. So 80 is the value of our percent
    3. But we need to make sure we put the percent symbol, %, after the 80 to show that it's a percent!
    1. We can plug our answer back into the original equation to make sure it's correct
    1. 'x' is the variable representing the percent
    2. '%' stands for percent
    1. We can't multiply percents, so we need to change 80% to a decimal first
    2. Just move the decimal point to the left two places and drop the percent symbol
    1. Since we got the same thing on both sides, our answer must be correct!