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Practice set e

It takes person A 4 hours less than person B to complete a certain task. Working together, both can complete the task in 8 3 hours. How long does it take each person to complete the task working alone?

Step 1:

Step 2:





Step 3:





Step 4:



Step 5:

Person A, 4 hr to complete the task; person B, 8 hr complete the task.

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Sample set f

The width of a rectangle is 1 3 its length. Find the dimensions (length and width) if the perimeter is 16 cm.

Step 1:  Let x = length. Then, x 3 = width.

Step 2:  Make a sketch of the rectangle.
A rectangle with the length as
The perimeter of a figure is the total length around the figure.
x + x 3 + x + x 3 = 16 2 x + 2 x 3 = 16 Step 3: 2 x + 2 x 3 = 16. The LCD is 3 . 3 · 2 x + 3 · 2 x 3 = 3 · 16 6 x + 2 x = 48 8 x = 48 x = 6 Check this potential solution . Step 4: 6 + 6 3 + 6 + 6 3 = 16 Is this correct? 6 + 2 + 6 + 2 = 16 Is this correct? 16 = 16 Yes, this is correct. Since  x = 6 , x 3 = 6 3 = 2 Step 5 : The length = 6 cm and the width = 2 cm .

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Practice set f

The width of a rectangle is 1 12 its length. Find the dimensions (length and width) if the perimeter is 78 feet.

Step 1:



Step 2:




Step 3:




Step 4:



Step 5:

length = 36 ft, width = 3 ft.

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Exercises

For the following problems, solve using the five-step method.

When the same number is added to both the numerator and denominator of the fraction 3 7 , the result is 2 3 . What is the number?

The number added is 5.

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When the same number is added to both the numerator and denominator of the fraction 5 8 , the result is 3 4 . What is the number?

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When the same number is added to both the numerator and denominator of the fraction 3 8 , the result is 1 6 . What is the number?

The number added is 2.

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When the same number is added to both the numerator and denominator of the fraction 7 9 , the result is 2 3 . What is the number?

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When the same number is subtracted from both the numerator and denominator of 1 10 , the result is 2 3 . What is the number?

The number subtracted is 17.

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When the same number is subtracted from both the numerator and denominator of 3 4 , the result is 5 6 . What is the number?

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One third of a number added to the reciprocal of number yields 13 6 . What is the number?

x = 1 2 , 6

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Four fifths of a number added to the reciprocal of number yields 81 10 . What is the number?

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One half of a number added to twice the reciprocal of the number yields 2. What is the number?

2

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One fourth of a number added to four times the reciprocal of the number yields 10 3 . What is the number?

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One inlet pipe can fill a tank in 8 hours. Another inlet pipe can fill the tank in 5 hours. How long does it take both pipes working together to fill the tank?

3 1 13  hours

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One pipe can drain a pool in 12 hours. Another pipe can drain the pool in 15 hours. How long does it take both pipes working together to drain the pool?

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A faucet can fill a bathroom sink in 1 minute. The drain can empty the sink in 2 minutes. If both the faucet and drain are open, how long will it take to fill the sink?

two minutes

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A faucet can fill a bathtub in 6 1 2 minutes. The drain can empty the tub in 8 1 3 minutes. If both the faucet and drain are open, how long will it take to fill the bathtub?

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An inlet pipe can fill a tank in 5 hours. An outlet pipe can empty the tank in 4 hours. If both pipes are open, can the tank be filled? Explain.

No. x = 20 hours.

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Questions & Answers

what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
how did I we'll learn this
Noor Reply
f(x)= 2|x+5| find f(-6)
Prince Reply
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
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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