Problem
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false) Explain your reasoning The price of tuition has quintupled since my parents went to school that's a $400 \%$ increase in price Choose the correct answer below. A. The statement makes sense. The percent increase is always divided by 80 to find the factor by which the original price has changed. B. The statement does not make sense. If the tuition quintuples, then the price increases by $500 \%$. C. The statement makes sense A $400 \%$ increase in price corresponds to a price that is $500 \%$ of the original price D. The statement does not make sense. If the tuition quintuples, then the price increases by $300 \%$.
Solution
Step 1 ：The statement is saying that the tuition price has quintupled, which means it has increased by a factor of 5. In terms of percentage, this is a 400% increase because the original price is considered 100%, and each additional original price added is another 100%. So, four additional original prices (which makes the price quintuple) is a 400% increase.
Step 2 ：Therefore, the statement makes sense and the correct answer is \(\boxed{\text{C. The statement makes sense. A $400 \%$ increase in price corresponds to a price that is $500 \%$ of the original price}}\).
