# 3.2 Solve percent applications  (Page 7/18)

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Find the amount of mark-up and the list price.

Jim’s music store bought a guitar at original cost $1,200. Jim marked the price up 50%.$600 $1,800 Find the amount of mark-up and the list price. The Auto Resale Store bought Pablo’s Toyota for$8,500. They marked the price up 35%.

$2,975$11,475

## Key concepts

• Percent Increase To find the percent increase:
1. Find the amount of increase. $\text{increase}=\text{new amount}-\text{original}\phantom{\rule{0.2em}{0ex}}\text{amount}$
2. Find the percent increase. Increase is what percent of the original amount?
• Percent Decrease To find the percent decrease:
1. Find the amount of decrease. $\text{decrease}=\text{original amount}-\text{new}\phantom{\rule{0.2em}{0ex}}\text{amount}$
2. Find the percent decrease. Decrease is what percent of the original amount?
• Simple Interest If an amount of money, P , called the principal, is invested for a period of t years at an annual interest rate r , the amount of interest, I, earned is
$\begin{array}{ccc}\hfill I& =\hfill & Prt\hfill \\ \hfill \text{where}\phantom{\rule{1em}{0ex}}I& =\hfill & \text{interest}\hfill \\ \hfill P& =\hfill & \text{principal}\hfill \\ \hfill r& =\hfill & \text{rate}\hfill \\ \hfill t& =\hfill & \text{time}\hfill \end{array}$
• Discount
• amount of discount is discount rate $·$ original price
• sale price is original price – discount
• Mark-up
• amount of mark-up is mark-up rate $·$ original cost
• list price is original cost + mark up

## Practice makes perfect

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What number is 45% of 120?

54

What number is 65% of 100?

What number is 24% of 112?

26.88

What number is 36% of 124?

250% of 65 is what number?

162.5

150% of 90 is what number?

800% of 2250 is what number?

18,000

600% of 1740 is what number?

28 is 25% of what number?

112

36 is 25% of what number?

81 is 75% of what number?

108

93 is 75% of what number?

8.2% of what number is $2.87?$35

6.4% of what number is $2.88? 11.5% of what number is$108.10?

$940 12.3% of what number is$92.25?

What percent of 260 is 78?

30%

What percent of 215 is 86?

What percent of 1500 is 540?

36%

What percent of 1800 is 846?

30 is what percent of 20?

150%

50 is what percent of 40?

840 is what percent of 480?

175%

790 is what percent of 395?

Solve Percent Applications

In the following exercises, solve.

Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16% of the total bill as a tip. How much should the tip be?$11.88

When Hiro and his co-workers had lunch at a restaurant near their work, the bill was $90.50. They want to leave 18% of the total bill as a tip. How much should the tip be? Trong has 12% of each paycheck automatically deposited to his savings account. His last paycheck was$2165. How much money was deposited to Trong’s savings account?

$259.80 Cherise deposits 8% of each paycheck into her retirement account. Her last paycheck was$1,485. How much did Cherise deposit into her retirement account?

One serving of oatmeal has eight grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?

24.2 g

One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

A bacon cheeseburger at a popular fast food restaurant contains 2070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?

2407 mg

integer greater than 2 and less than 12
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
He charges $125 per job. His monthly expenses are$1,600. How many jobs must he work in order to make a profit of at least $2,400? Alicia Reply at least 20 Ayla what are the steps? Alicia 6.4 jobs Grahame 32 Grahame 1600+2400= total amount with expenses. 4000/125= number of jobs needed to make that min profit of 2400. answer is 32 Orlando He must work 32 jobs to make a profit POP what is algebra Azhar Reply repeated addition and subtraction of the order of operations. i love algebra I'm obsessed. Shemiah hi Krekar One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag? Leanna Reply they are 92 candies in the bag POP rectangular field solutions Navin Reply What is this? Donna t muqtaar the proudact of 3x^3-5×^2+3 and 2x^2+5x-4 in z7[x]/ is anas Reply ? Choli a rock is thrown directly upward with an initial velocity of 96feet per second from a cliff 190 feet above a beach. The hight of tha rock above the beach after t second is given by the equation h=_16t^2+96t+190 Usman Stella bought a dinette set on sale for$725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount? Manhwa Reply 44.19% Scott 40.22% Terence 44.2% Orlando I don't know Donna if you want the discounted price subtract$725 from $1299. then divide the answer by$1299. you get 0.4419... but as percent you get 44.19... but to the nearest tenth... round .19 to .2 and you get 44.2%
Orlando
you could also just divide $725/$1299 and then subtract it from 1. then you get the same answer.
Orlando
p mulripied-5 and add 30 to it
Tausif
Tausif
how
muqtaar
Can you explain further
p mulripied-5 and add to 30
Tausif
-5p+30?
Corey
p=-5+30
Jacob
How do you find divisible numbers without a calculator?
TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13
BAINAMA
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was$1,585. What is the amount of each loan?
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus?
66miles/hour
snigdha
How did you work it out?
Esther
s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr
Orlando
No; 65m/hr
albert
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
what do you need help in?
Felix
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found$7(+7). Totally you lost just $12 (-12) Annushka I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-\$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
hi
albert
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce