Questions
\(\textbf{1)}\) Jessica collects rocks. She started the week with 20 rocks. Later in the week she traded 3 of her rocks to Steve for 12 of his rocks. She then sold 5 to her brother. After all of this, what is the percent of increase in Jessica’s rock collection?
Jessica’s rock collection increased by \( 20\% \).
\(\textbf{2)}\) One day, a stock increases in value by 25%. The next day it decreases by 25%. By what percent did the value of the stock change after both days?
The stock is only worth \( 93.75\% \) of its original value.
\(\textbf{3)}\) Harry wanted to buy a book that cost $20 last week. This week he came back and it cost $25. What was the percent change (magnitude and direction) in the price of the book? Show your work.
\(\text{Percent Change} = \displaystyle \frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\)
\(\displaystyle \frac{25-20}{20}=\frac{5}{20}=\frac{1}{4}=.25=25\%\)
Increase of \(25\%\)
\(\textbf{4)}\) Harry waited on the $25 book. It was just too expensive for him. But after Christmas, he saw that it was on sale for $20. What was the percent change (magnitude and direction) in the price of the book? Show your work.
\(\text{Percent Change} = \displaystyle \frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\)
\(\displaystyle \frac{20-25}{25}=\frac{-5}{25}=\frac{-1}{5}=-.20=20\%\)
Decrease of \(20\%\)
\(\textbf{5)}\) You should have gotten different percent rates for questions 3 and 4 even though the amount of change in dollars is the same. Explain why the percent rates are different.
The dollar amount change was the same. ($5) But the original value changed. It increased from $20 in the first and decreased from $25 in the second. $5 out of $20 is a different percentage than $5 out of $25.
\(\textbf{6)}\) The price of an hour of babysitting was $7.50 in 2000. In 2010, the price was $15. What was the percent change (magnitude and direction) in the price of the babysitting? Show your work.
\(\text{Percent Change} = \displaystyle \frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\)
\(\displaystyle \frac{15-7.5}{7.5}=\frac{7.5}{7.5}=\frac{1}{1}=1=100\%\)
Increase of \(100\%\)
\(\textbf{7)}\) A compass decreased in price from $40 to $10 in the last 5 years. What was the percent change (magnitude and direction) in the price of the compass? Show your work.
\(\text{Percent Change} = \displaystyle \frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\)
\(\displaystyle \frac{10-40}{40}=\frac{-30}{40}=\frac{-3}{4}-.75=-75\%\)
Decrease of \(75\%\)
\(\textbf{8)}\) Sam has $100 in a stock. On Tuesday, the stock decreases 25% from the day before. Sam is unhappy with this. On Wednesday the stock increases 25% from the day before.Sam is happy again. Did Sam get all his money back?
No, Sam did not get his money back. His $100 is now $93.75.
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