Math 1010

Finance Unit

1.2 Percentages

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.
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.
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?
  $180-54=\$126$
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. If Sue gave away a fourth of her collection, how many DVDs would she have left?
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. If Sue gave away three fifths of her collection, how many coins would that be?

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}$
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.
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.
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.

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.
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.