Finance Unit

1.2 Percentages

  1. The jewelry store is having a 25% off sale. If an item regularly costs $80, what is the sale price?

    \(80\cdot0.25=20\)

    \(80-20=60\)

    The sale price is $60.

  2. Fred had a checking account which had $2500 in it at the first of April. Paying his federal income tax reduced his account by 15%. How much money is left in his account?

    \(2500\cdot0.15=375\)

    \(2500-375=2125\)

    Fred has $2125 left in his account.

  3. The jewelry store is having a 30% off sale.
    1. If the item regularly costs $180, what is the discount?

      \(0.30\cdot180=\$54\)

    2. What is the sale price?

      \(180-54=\$126\)

  4. Sue has a DVD collection. She has a total of 280 DVDs
    1. If 40% of Sue’s DVDs are action, how many action DVDs does she have?

      2. \(0.40\cdot280=112\) action DVDs

    2. If Sue gave away a fourth of her collection, how many DVDs would she have left?

      3. \( \frac14\cdot280=70\) DVDs

      \(280-70=210\) DVDs left.

  5. Sue has a coin collection. She has a total of 180 coins.
    1. If 20% of Sue’s coins are silver dollars, how many silver dollars does she have?

      2. \(0.20\cdot180=36\) silver dollars

    2. If Sue gave away three fifths of her collection, how many coins would that be?

      3. \( \frac35\cdot180=108\) coins

  6. Shannon’s teacher announced that 65% of the students in her history class passed the test.
    1. If there are 40 students in her class, how many passed the test?

      \(0.65\cdot40=26\) students

    2. What is the ratio of students who did NOT pass to students who did pass?

      \(40-26=14\) students did not pass the test

      \( \frac{14}{26}=\frac7{13}\)

  7. Probability is the long-term chance that a certain outcome will occur from some random process. What is the probability of a fair coin landing heads up when flipped? What is the probability that a person rolls a 3 when rolling a fair die? Write these probabilities as decimals and percentages.

    Probability of event A =\(\frac{\text{number of outcomes in event A}}{ \text{total number of events}} \)

    \( P(heads)= \frac{1}{2}=0.5=50\%\)

    \( P(3)= \frac{1}{6}=0.1667=16.67\%\)

  8. Suppose you flip a fair coin three times in a row. What is the probability that it lands on heads every time? Make a tree diagram to show the possible outcomes when flipping a coin three times in a row.

    tree diagram for tossing a coin 3 times. For the first toss, the possible outcomes are heads (H) or tails (T) for a total of 2 branches. For the second toss, the tree branches from the first H or T. There are two branches off the H, one an H and the other a T. There are also two branches off the T, one an H and the other a T. After the 2nd toss there are four branches. For the third toss, each of the 4 branches from the 2nd toss are branched with an H and a T, for a total of 8 branches. The sample space outcomes are listed: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

    \( P(3H)= \frac12\cdot\frac12\cdot\frac12=\frac18=0.125=12.5\%\)

  9. How many times would you expect a fair coin to land heads up if you flip the coin ten times in a row? Flip an actual coin ten times in a row and record the outcomes. Compare with your prediction. Why might they not be the same?

    5 times

    Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out.

  10. In the 2018-2019 regular season, NBA basketball player Steph Curry attempted 287 free throws and made 263 of them. What is the probability that Steph Curry will make a free throw? Write this probability as a fraction, as a decimal, and as a percentage.

    \( P(\text{Make})= \frac{263}{287}=0.9164=91.64\%\)

  11. Kingsport, TN has a population of 53,091 and had 2954 instances of violent and property crime in 2014. Knoxville, TN has a population of 185,638 and had 12,863 instances of violent and property crime in 2014. Which is the safer city? How many crimes occurred per 100 people in each city?

    Kingsport: \(\frac{2954}{53091}=0.0556=5.56\%=\frac{5.56}{100}\)

    Knoxville: \(\frac{12863}{185638}=0.0693=6.93\%=\frac{6.93}{100}\)

    Kingsport is the safer city.

  12. There are 400 boys and 420 girls in a school. If 18% of the boys are left-handed and 10% of the girls are left-handed, what percentage of students in the school are left-handed?

    18% of 400 boys = \(0.18 * 400 = 72\) left-handed boys

    10% of 420 girls = \(0.10 * 420 = 42\) left-handed girls

    \(72 + 42 = 114\) left-handed students

    \(\frac{114\;\text{ left handed}}{820\;\text{total students}}\) = 0.14

    14% of the students are left-handed.

  13. Is a discount of 30% off the original price, followed by a discount of 50% off the sale price, the same as a discount of 80% off the original price? (Hint: What would a $100 item cost after these discounts?)

    \(100\cdot0.30=30\)

    \(100-30=70\)

    \(70\cdot0.50=35\)

    \(70-35=35\)

    You will pay $35 for the item marked 30% off and then 50% off.

    \(100\cdot0.80=80\)

    \(100-80=20\)

    You will pay $20 for the item marked 80% off.

    They are not the same.

  14. Jacob has a part time job at Food City. He started out earning $7.50 an hour, but recently got a raise to $8.00 an hour. His mother, Amy, teaches full time at Pellissippi State. Her salary last year was $50,500. This year she got a raise and her current salary is $53,000. Who got the better raise?

    Jacob: \( \frac{8.00-7.50}{7.50}=\frac{0.50}{7.50}\approx0.067\approx6.7\%\)

    Amy: \( \frac{53000-50500}{50500}=\frac{2500}{50500}=0.05=5\%\)

    Jacob got the better raise.

  15. Last year a company made a net profit of $20,000 on sales of $1,000,000. This year they made a net profit of $40,000 on sales of $1,000,000. When talking to the shareholders, the company executives claimed that their profit increased by 100%, and asked for a bonus for doing so well. When talking to the union about a possible wage raise, the company executives claimed that their profit only increased by 2%, which hasn't even kept up with inflation. How did they determine these figures? Which one do you think is correct??

    The absolute change in profit is from $20,000 to $40,000 so it doubles.

    The profit percentage is 2% last year and 4% this year so the percentage also doubles.