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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

how did you get 1640
Noor Reply
If auger is pair are the roots of equation x2+5x-3=0
Peter Reply
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
MATTHEW Reply
420
Sharon
from theory: distance [miles] = speed [mph] × time [hours] info #1 speed_Dennis × 1.5 = speed_Wayne × 2 => speed_Wayne = 0.75 × speed_Dennis (i) info #2 speed_Dennis = speed_Wayne + 7 [mph] (ii) use (i) in (ii) => [...] speed_Dennis = 28 mph speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5. Substituting the first equation into the second: W * 2 = (W + 7) * 1.5 W * 2 = W * 1.5 + 7 * 1.5 0.5 * W = 7 * 1.5 W = 7 * 3 or 21 W is 21 D = W + 7 D = 21 + 7 D = 28
Salma
Devon is 32 32​​ years older than his son, Milan. The sum of both their ages is 54 54​. Using the variables d d​ and m m​ to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
Aaron Reply
find product (-6m+6) ( 3m²+4m-3)
SIMRAN Reply
-42m²+60m-18
Salma
what is the solution
bill
how did you arrive at this answer?
bill
-24m+3+3mÁ^2
Susan
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
hi
Bajemah
-6m(3mA²+4m-3)+6(3mA²+4m-3) =-18m²A²-24m²+18m+18mA²+24m-18 Rearrange like items -18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph. 1.x+2y=3
Jovelyn Reply
x=3-2y
Salma
y=x+3/2
Salma
Hi
Enock
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
3x-12y=18
Kelvin
please why isn't that the 0is in ten thousand place
Grace Reply
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
Marry Reply
how far
Abubakar
cool u
Enock
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
Abegail Reply
hello
BenJay
hi
Method
I am eliacin, I need your help in maths
Rood
how can I help
Sir
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
cameron Reply
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
mahnoor Reply
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67. Check: Sales = 3542 Commission 12%=425.04 Pay = 500 + 425.04 = 925.04. 925.04 > 925.00
Munster
difference between rational and irrational numbers
Arundhati Reply
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
Jakoiya Reply
how to reduced echelon form
Solomon Reply
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
Zack Reply
d=r×t the equation would be 8/r+24/r+4=3 worked out
Sheirtina
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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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