Math 1010

Finance Unit

1.2 Percentages

Statistically, 44% of students who start at a community college graduate with a degree. If 100 students enroll at a community college, how many are expected to earn a degree?
$100\cdot0.44=44$
In Fall 2026, 2500 first time freshmen enrolled at Pellissippi State. If 44% earn a degree, how many of these freshmen will go on to graduate?
$2500\cdot0.44=1100$
The jewelry store is having a 25% off sale. If a necklace regularly costs $80, what is the sale price?
$80\cdot0.25=20$

$80-20=60$

The sale price is $60.
Hayden had a checking account which had $3200 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?
$3200\cdot0.15=480$

$3200-480=2720$

Fred has $2720 left in his account.
Kingsport, TN has a population of 57,500 and risk models predict about 2200 instances of violent and property crime per year. Knoxville, TN has a population of 202,021 and risk models predict about 9502 instances of violent and property crime per year. Which is the safer city? How many crimes occurred per 100 people in each city?
Kingsport: $\frac{2200}{57500}=0.0382=3.82\%$ which is 3.8 crimes per 100 people.

Knoxville: $\frac{9502}{202021}=0.0470=4.7\%$ which is 4.7 crimes per 100 people.

Kingsport is the safer city.
Jasmine earns $950 per month at a part-time job. She spends $80 a month for gasoline and $375 per month for groceries. What percentage of her wages does she spend on gas and groceries?
$\frac{455}{950}=0.4789=47.9\%$
Pellissippi State enrollment increased from 9312 students in 2024 to 9718 students in 2025. What was the percent increase in enrollment?
$\frac{406}{9312}=0.0436=4.4\%$
The jewelry store is having a 30% off sale.
1. If a bracelet regularly costs $180, what is the discount?
  $0.30\cdot180=\$54$
2. What is the sale price?
  $180-54=\$126$
3. What is the sale price including 9.25% sales tax?
  $126\cdot0.0925=11.66$
  
  $126+11.66=$137.66$
The jewelry store reduced the price of a diamond ring from $900 to $720. What was the percent decrease?
$\frac{720-900}{900}=-0.2=20\%$ decrease

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}$
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 $9.50 an hour, but recently got a raise to $10.00 an hour. His mother, Amy, teaches full time at Pellissippi State. Her salary last year was $70,500. This year she got a raise and her current salary is $73,000. What was the percent increase in each of their paychecks?
Jacob: $ \frac{10.00-9.50}{9.50}=\frac{0.50}{9.50}=0.0526=5.3\%$

Amy: $ \frac{73000-70500}{70500}=\frac{2500}{70500}=0.0354=3.5\%$