<< Chapter < Page Chapter >> Page >

Andreas bought a used car for $12,000. Because the car was 4-years old, its price was 3 4 of the original price, when the car was new. What was the original price of the car?

Solution

What are you asked to find? The original price of the car Assign a variable. Let p = the original price . Write a sentence that gives the information to find it. $12,000 is 3 4 of the original price. Translate into an equation. Solve. 12,000 = 3 4 p 4 3 ( 12,000 ) = 4 3 · 3 4 p 16,000 = p The original cost of the car was $16,000. Check: Is 3 4 of $16,000 equal to $12,000? 3 4 · 16,000 = ? 12,000 12,000 = 12,000

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate and solve:

The annual property tax on the Mehta’s house is $1,800, calculated as 15 1,000 of the assessed value of the house. What is the assessed value of the Mehta’s house?

$120,000

Got questions? Get instant answers now!

Translate and solve:

Stella planted 14 flats of flowers in 2 3 of her garden. How many flats of flowers would she need to fill the whole garden?

21 flats

Got questions? Get instant answers now!

Key concepts

  • The Division Property of Equality —For any numbers a , b , and c , and c 0 , if a = b , then a c = b c .
    When you divide both sides of an equation by any non-zero number, you still have equality.
  • The Multiplication Property of Equality —For any numbers a , b , and c , if a = b , then a c = b c .
    If you multiply both sides of an equation by the same number, you still have equality.

Practice makes perfect

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution.

−809 = 15 y

y = 809 15

Got questions? Get instant answers now!

−37 p = −541

p = 541 37

Got questions? Get instant answers now!

5 8 w = 40

w = −64

Got questions? Get instant answers now!

2 5 = 1 10 a

a = −4

Got questions? Get instant answers now!

7 10 x = 14 3

x = 20 3

Got questions? Get instant answers now!

7 12 = 3 4 p

p = 7 9

Got questions? Get instant answers now!

5 18 = 10 9 u

u = 1 4

Got questions? Get instant answers now!

Solve Equations That Require Simplification

In the following exercises, solve each equation requiring simplification.

100 16 = 4 p 10 p p

p = −12

Got questions? Get instant answers now!

−18 7 = 5 t 9 t 6 t

Got questions? Get instant answers now!

7 8 n 3 4 n = 9 + 2

n = 88

Got questions? Get instant answers now!

5 12 q + 1 2 q = 25 3

Got questions? Get instant answers now!

0.25 d + 0.10 d = 6 0.75

d = 15

Got questions? Get instant answers now!

0.05 p 0.01 p = 2 + 0.24

Got questions? Get instant answers now!

−10 ( q 4 ) 57 = 93

q = −11

Got questions? Get instant answers now!

−12 ( d 5 ) 29 = 43

Got questions? Get instant answers now!

−10 ( x + 4 ) 19 = 85

x = 72 5

Got questions? Get instant answers now!

−15 ( z + 9 ) 11 = 75

Got questions? Get instant answers now!

Mixed Practice

In the following exercises, solve each equation.

c 0.3 c = 35.70

c = 51

Got questions? Get instant answers now!

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

187 is the product of −17 and m .

Got questions? Get instant answers now!

133 is the product of −19 and n .

133 = −19 n ; n = −7

Got questions? Get instant answers now!

−184 is the product of 23 and p .

Got questions? Get instant answers now!

−152 is the product of 8 and q .

−152 = 8 q ; q = −19

Got questions? Get instant answers now!

u divided by 7 is equal to −49 .

Got questions? Get instant answers now!

r divided by 12 is equal to −48 .

r 12 = −48 ; r = −576

Got questions? Get instant answers now!

h divided by −13 is equal to −65 .

Got questions? Get instant answers now!

j divided by −20 is equal to −80 .

j −20 = −80 ; j = 1,600

Got questions? Get instant answers now!

The quotient c and −19 is 38.

Got questions? Get instant answers now!

The quotient of b and −6 is 18.

b −6 = 18 ; b = −108

Got questions? Get instant answers now!

The quotient of h and 26 is −52 .

Got questions? Get instant answers now!

The quotient k and 22 is −66 .

k 22 = −66 ; k = −1,452

Got questions? Get instant answers now!

Three-tenths of x is 15.

3 10 x = 15 ; x = 50

Got questions? Get instant answers now!

Five-halves of v is 50.

5 2 v = 50 ; v = 20

Got questions? Get instant answers now!

The sum of nine-tenths and g is two-thirds.

Got questions? Get instant answers now!

The sum of two-fifths and f is one-half.

2 5 + f = 1 2 ; f = 1 10

Got questions? Get instant answers now!

The difference of p and one-sixth is two-thirds.

Got questions? Get instant answers now!

The difference of q and one-eighth is three-fourths.

q 1 8 = 3 4 ; q = 7 8

Got questions? Get instant answers now!

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?

Got questions? Get instant answers now!

Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. How many balloons did she use in each bunch?

6 balloons

Got questions? Get instant answers now!

Tickets Mollie paid $36.25 for 5 movie tickets. What was the price of each ticket?

Got questions? Get instant answers now!

Shopping Serena paid $12.96 for a pack of 12 pairs of sport socks. What was the price of pair of sport socks?

$1.08

Got questions? Get instant answers now!

Sewing Nancy used 14 yards of fabric to make flags for one-third of the drill team. How much fabric, would Nancy need to make flags for the whole team?

Got questions? Get instant answers now!

MPG John’s SUV gets 18 miles per gallon (mpg). This is half as many mpg as his wife’s hybrid car. How many miles per gallon does the hybrid car get?

36 mpg

Got questions? Get instant answers now!

Height Aiden is 27 inches tall. He is 3 8 as tall as his father. How tall is his father?

Got questions? Get instant answers now!

Real estate Bea earned $11,700 commission for selling a house, calculated as 6 100 of the selling price. What was the selling price of the house?

$195,000

Got questions? Get instant answers now!

Everyday math

Commission Every week Perry gets paid $150 plus 12% of his total sales amount. Solve the equation 840 = 150 + 0.12 ( a 1250 ) for a , to find the total amount Perry must sell in order to be paid $840 one week.

Got questions? Get instant answers now!

Stamps Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation 0.49 s + 0.21 ( s 5 ) = 9.45 for s , to find the number of 49-cent stamps Travis bought.

15 49-cent stamps

Got questions? Get instant answers now!

Writing exercises

Frida started to solve the equation −3 x = 36 by adding 3 to both sides. Explain why Frida’s method will not solve the equation.

Got questions? Get instant answers now!

Emiliano thinks x = 40 is the solution to the equation 1 2 x = 80 . Explain why he is wrong.

Answers will vary.

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has five rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can...,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can...” reads “1) solve equations using the Division and Multiplication Properties of equality,” “2) solve equations that require simplification,” “3) translate to an equation and solve,” and “4) translate and solve applications.” The rest of the cells are blank.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask