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By the end of this section, you will be able to:
  • Translate and solve basic percent equations
  • Solve applications of percent
  • Find percent increase and percent decrease

Before you get started, take this readiness quiz.

  1. Translate and solve: 3 4 of x is 24 .
    If you missed this problem, review Solve Equations with Fractions .
  2. Simplify: ( 4.5 ) ( 2.38 ) .
    If you missed this problem, review Decimal Operations .
  3. Solve: 3.5 = 0.7 n .
    If you missed this problem, review Solve Equations with Decimals .

Translate and solve basic percent equations

We will solve percent equations by using the methods we used to solve equations with fractions or decimals. In the past, you may have solved percent problems by setting them up as proportions. That was the best method available when you did not have the tools of algebra. Now as a prealgebra student, you can translate word sentences into algebraic equations, and then solve the equations.

We'll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application.

When Aolani and her friends ate dinner at a restaurant, the bill came to $80 . They wanted to leave a 20% tip. What amount would the tip be?

To solve this, we want to find what amount is 20% of $80 . The $80 is called the base . The amount of the tip would be 0.20 ( 80 ) , or $16 See [link] . To find the amount of the tip, we multiplied the percent by the base.

The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.
A 20% tip for an $80 restaurant bill comes out to $16 .

In the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.

What number is 35% of 90 ?

Solution

Translate into algebra. Let n = the number. .
Multiply. 31.5 is 35% of 90
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What number is 45% of 80 ?

36

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What number is 55% of 60 ?

33

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125% of 28 is what number?

Solution

Translate into algebra. Let a = the number. .
Multiply. 125% of 28 is 35 .

Remember that a percent over 100 is a number greater than 1 . We found that 125% of 28 is 35 , which is greater than 28 .

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150% of 78 is what number?

117

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175% of 72 is what number?

126

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In the next examples, we are asked to find the base.

Translate and solve: 36 is 75% of what number?

Solution

Translate. Let b = the number. .
Divide both sides by 0.75. .
Simplify. .
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17 is 25% of what number?

68

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40 is 62.5% of what number?

64

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6.5% of what number is $1.17 ?

Solution

Translate. Let b = the number. .
Divide both sides by 0.065. .
Simplify. .
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7.5% of what number is $1.95 ?

$26

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8.5% of what number is $3.06 ?

$36

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In the next examples, we will solve for the percent.

What percent of 36 is 9 ?

Solution

Translate into algebra. Let p = the percent. .
Divide by 36. .
Simplify. .
Convert to decimal form. .
Convert to percent. .
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What percent of 76 is 57 ?

75%

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What percent of 120 is 96 ?

80%

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144 is what percent of 96 ?

Solution

Translate into algebra. Let p = the percent. .
Divide by 96. .
Simplify. .
Convert to percent. .
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110 is what percent of 88 ?

125%

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126 is what percent of 72 ?

175%

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Solve applications of percent

Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Good
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 2

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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