In Grade 6-Fuchsia, 24 teenagers prefer dancing to singing. If this represented 80% of the respondents, how many respondents were there in all?
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Base, Rate, Percentage Word Problem
80% of ____ is 24
Given:
Rate = 80%
Percentage = 24
Base = ?
Asked: Total respondents or base
Solutions:
Base (Total respondents) =
Base (Total respondents) =
Base (Total respondents) = 30
Answer: There were 30 total respondents.
Step-by-step explanation:
Percent is the result when a number is multiplied by a percent. One clue to identifying the percent is that it comes after the word is. Base is the whole in the problem or equation. This is the amount you are taking a percent of. One clue in identifying the base is that it comes after the word of. Rate is the ratio of the amount to the base. It is written as a percent (%). Thus, in the question, 80% of ____ is 24, 80% is the rate and 24 is the percentage. What is missing is the base.
These three quantities are connected to each other in terms of the computation. The following are the formula to be used:
Percentage (P) = Base (B) x Rate (R)
Rate (R) = Percentage (P) / Base (B)
Base (B) = Percentage (P) / Rate (R)
Remember that the rate must be changed from a percent to a decimal before multiplying can be done.
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