Math 1010

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?

   $0.40\cdot280=112$ action DVDs

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

   $\frac14\cdot280=70$ 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?

   $0.20\cdot180=36$ silver dollars

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

   $\frac35\cdot180=108$ 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. 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.

8. 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.

9. 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.

10. 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.

11. 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.