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Some phrases and sentences do not translate directly. We must be careful to read them properly. The word from often appears in such phrases and sentences. The word from means "a point of departure for motion." The following translation will illustrate this use.

The translation of a verbal expressions 'Fifteen is subtracted from some quantity' into mathematical expressions is x minus fifteen.

The word from indicates the motion (subtraction) is to begin at the point of "some quantity."

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Eight less than some quantity. Notice that less than could be replaced with from .
x 8

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Practice set b

Translate the following phrases and sentences into mathematical expressions or equations.

A number divided by sixteen, plus one, is five.

x 16 + 1 = 5

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Seven times two more than a number is twenty-one.

7 ( 2 + x ) = 21

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A number divided by two more than itself is zero.

x 2 + x = 0

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A number minus five is divided by twice the number plus three and the result is seventeen.

x 5 2 x + 3 = 17

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Fifty-two is subtracted from some quantity.

x 52

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An unknown quantity is subtracted from eleven and the result is five less than the unknown quantity.

11 x = x 5

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Exercises

For the following problems, translate the following phrases or sentences into mathematical expressions or equations.

A quantity less four.

a 4

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Eight more than a number.

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A number plus seven.

b + 7

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Negative five plus an unknown quantity.

5 + c

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Negative sixteen minus some quantity.

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Fourteen added to twice a number.

2 d + 14

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Ten added to three times some number.

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One third minus an unknown quantity.

1 3 e

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Twice a number is eleven.

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Four ninths of a number is twenty-one.

4 9 f = 21

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One third of a number is two fifths.

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Three times a number is nine more than twice the number.

3 g = 2 g + 9

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Five times a number is that number minus two.

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Twice a number added to six results in thirty.

2 h + 6 = 30

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Ten times a number less four results in sixty-six.

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A number less twenty-five is equal to 3.019 .

k 25 = 3.019

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Seven more than some number is five more than twice the number.

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When a number is divided by four, the result is sixty-eight.

m 4 = 68

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Eleven fifteenths of two more than a number is eight.

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One tenth of a number is that number less one.

n 10 = n 1

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Two more than twice a number is one half the number less three.

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A number is equal to itself plus four times itself.

x = x + 4 x

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Three fifths of a quantity added to the quantity itself is thirty-nine.

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A number plus seven is divided by two and the result is twenty-two.

Q + 7 2 = 22

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Ten times a number minus one is divided by fourteen and the result is one.

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A number is added to itself then divided by three. This result is then divided by three. The entire result is fifteen.

r + r 3 3 = 15

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Ten divided by two more than a number is twenty-one.

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Five divided by a number plus six is fourteen.

5 s + 6 = 14

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Twelve divided by twice a number is fifty-five.

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Twenty divided by eight times a number added to one is nine.

20 8 x + 1 = 9

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A number divided by itself, plus one, results in seven.

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A number divided by ten, plus four, results in twenty-four.

v 10 + 4 = 24

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A number plus six, divided by two, is seventy-one.

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A number plus six, divided by two, plus five, is forty-three.

w + 6 2 + 5 = 43

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A number multiplied by itself added to five is thirty-one.

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A quantity multiplied by seven plus twice itself is ninety.

7 y + 2 y = 90

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A number is increased by one and then multiplied by five times itself. The result is eighty-four.

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A number is added to six and that result is multiplied by thirteen. This result is then divided by six times the number. The entire result is equal to fifty-nine.

( z + 16 ) 13 6 z = 59

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A number is subtracted from ten and that result is multiplied by four. This result is then divided by three more than the number. The entire result is equal to six.

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An unknown quantity is decreased by eleven. This result is then divided by fifteen. Now, one is subtracted from this result and five is obtained.

x 11 15 1 = 5

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Ten less than some number.

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Five less than some unknown number.

n 5

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Twelve less than a number.

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One less than an unknown quantity.

m 1

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Sixteen less than some number is forty-two.

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Eight less than some unknown number is three.

p 8 = 3

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Seven is added to ten less than some number. The result is one.

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Twenty-three is divided by two less than twice some number and the result is thirty-four.

23 2 n 2 = 34

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One less than some number is multiplied by three less than five times the number and the entire result is divided by six less than the number. The result is twenty-seven less than eleven times the number.

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Exercises for review

( [link] ) Supply the missing word. The point on a line that is associated with a particular number is called the of that number.

graph

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( [link] ) Supply the missing word. An exponent records the number of identical in a multiplication.

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( [link] ) Write the algebraic definition of the absolute value of the number a .

| a | = { a , i f a 0 a , i f a < 0

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( [link] ) Solve the equation 4 y + 5 = 3 .

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( [link] ) Solve the equation 2 ( 3 x + 1 ) 5 x = 4 ( x 6 ) + 17 .

x = 3

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Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
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Lambiv
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how is the graph works?I don't fully understand
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Lambiv
multiple choice question
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appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
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Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
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what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
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Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
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Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
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Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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