Of the 600 people at a music festival, 420 had attended the previous year. How many people out of 100 had attended the previous year?
Understand the Problem
The question is asking to calculate the number of people out of 100 who attended the previous year's music festival, given that 420 out of 600 people attended the previous year. This is a ratio problem, requiring us to determine what proportion of 100 corresponds to the same proportion of 420 out of 600.
Answer
70
Answer for screen readers
70
Steps to Solve
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Set up a proportion We can set up a proportion to solve this problem. The proportion can be written as: $$ \frac{420}{600} = \frac{x}{100} $$ where $x$ is the number of people out of 100 who attended the previous year.
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Solve for x To solve for $x$, we can cross-multiply: $$ 420 \cdot 100 = 600 \cdot x $$ $$ 42000 = 600x $$
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Isolate x Divide both sides by 600: $$ x = \frac{42000}{600} $$
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Simplify $$ x = \frac{420}{6} $$ $$ x = 70 $$
70
More Information
The answer to the question is 70. This means that if there were only 100 people at the music festival, 70 of them would have attended the previous year, based on the given ratio of attendees.
Tips
A common mistake is to set up the proportion incorrectly, for example $\frac{600}{420} = \frac{x}{100}$ or $\frac{420}{100} = \frac{x}{600}$. Another mistake might occur during the simplification process, leading to an incorrect value for $x$.
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