Notes
Questions
\(\textbf{1)}\) A sweater costs \($30\) and a shirt costs \($12\). During a \(10\%\) off sale, how much more does the sweater cost than the shirt?
The answer is \( $16.20 \)
\(\textbf{2)}\) A number added to \(30\%\) of the same number is \(52\). What is the number?
The answer is \( 40 \)
\(\textbf{3)}\) 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?
The answer is \( 20\% \)
\(\textbf{4)}\) A hat is on sale for \(15\%\) off the original price. The sale price is \($34.00\). What is the original price?
The answer is \( $40.00 \)
\(\textbf{5)}\) A cookie jar is half full. After adding \(6\) cookies it is \(75\%\) full. How many cookies can the jar hold if it is completely full?
The answer is \( 24\) cookies
\(\textbf{6)}\) At a school, exactly \(410\) students are seniors. \(40\%\) of the students at the school are seniors. How many students attend the school in total?
The answer is \( 1025\) students
\(\textbf{7)}\) If \(45\%\) of \(200\) is equal to \(300\%\) of x. What is x?
The answer is x \( =30 \)
\(\textbf{8)}\) What is the total price on a \($45.95\) sweater with \(7\%\) sales tax?
The answer is \( $49.17 \)
\(\textbf{9)}\) A hat that originally costs \($20\) is on sale for \(20\%\) off. What is the sale price?
The answer is \( $16 \)
\(\textbf{10)}\) Anna got paid $714. They took out \($152\) in taxes. What percent of her income was taken out for taxes?
The answer is \(\frac{152}{714} \approx 21.3\%\)
\(\textbf{11)}\) A TV normally costs \($600\). You have a \(15\%\) off coupon. How much is the TV after the coupon is applied?
The answer is \($510\)
\(\textbf{12)}\) A hat originally cost $40. It was on sale for 25% off, but there is 7% sales tax added to the sales price. You have saved $32. Do you have enough money saved to buy the hat? If yes, how much extra do you have? If no, how much will you need to borrow?
Discount amount\(\Rightarrow .25 \cdot 40=10\)
New Price\(\Rightarrow 40-10=30 \)
Tax amount\(\Rightarrow .07 \cdot 30=2.1 \)
Price after tax\(\Rightarrow 30+2.1=32.1\)
The hat costs $32.10.
I do not have enough money to buy the hat.
Borrow Amount\(\Rightarrow \left(32.1-32=.1\right)\)
I will need to borrow $.10 to buy the hat.
\(\textbf{13)}\) Steve saved $20 on a sweater that was marked down 62.5%. How much did he pay (what was the sale price)? What was the original price?
\(\displaystyle \frac{62.5}{100}=\frac{20}{x}\)
\((62.5) \cdot (x)=(20) \cdot (100) \)
\(62.5x=2000\)
\(\displaystyle \frac{62.5x}{62.5}=\frac{2000}{62.5} \)
\(x=32\)
Original price was \( \$32\)
\((32-20=12)\)
Steve Paid \( \$12\)
\(\textbf{14)}\) 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 \(25\%\)
\(\textbf{15)}\) 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 game? 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 \(20\%\)
\(\textbf{16)}\) 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 \(100\%\)
\(\textbf{17)}\) A toy 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 toy? 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 \(75\%\)
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