# 5.5 Application ii - solving problems  (Page 2/4)

 Page 2 / 4

## Practice set d

Garden A produces $5.8$ times as many vegetables as garden B. Together the gardens produce 102 pounds of vegetables. How many pounds of vegetables does garden A produce?

1. Let $x=$

Garden A produces 87 pounds of vegetables.

## Sample set e

Two consecutive even numbers sum to 432. What are the two numbers?

$\begin{array}{ll}\text{Step}\text{\hspace{0.17em}}\text{1:}\hfill & \text{Let}\text{\hspace{0.17em}}x=\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{smaller}\text{\hspace{0.17em}}\text{even}\text{\hspace{0.17em}}\text{number}\text{.}\text{\hspace{0.17em}}\text{Then}\text{\hspace{0.17em}}x+2=\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{next}\text{\hspace{0.17em}}\text{(consecutive)}\text{\hspace{0.17em}}\text{even}\text{\hspace{0.17em}}\text{number}\hfill \\ \hfill & \text{since}\text{\hspace{0.17em}}\text{consecutive}\text{\hspace{0.17em}}\text{even}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{differ}\text{\hspace{0.17em}}\text{by}\text{\hspace{0.17em}}\text{2}\text{\hspace{0.17em}}\text{(as}\text{\hspace{0.17em}}\text{do}\text{\hspace{0.17em}}\text{consecutive}\text{\hspace{0.17em}}\text{odd}\text{\hspace{0.17em}}\text{numbers)}\text{.}\hfill \end{array}$
$\begin{array}{lllll}\text{Step}\text{\hspace{0.17em}}\text{2:}\hfill & \hfill x+x+2& =\hfill & 432.\hfill & \hfill \\ \text{Step}\text{\hspace{0.17em}}\text{3:}\hfill & \hfill x+x+2& =\hfill & 432\hfill & \hfill \\ \hfill & \hfill 2x+2& =\hfill & 432\hfill & \hfill \\ \hfill & \hfill 2x& =\hfill & 430\hfill & \hfill \\ \hfill & \hfill x& =\hfill & 215.\hfill & \text{Also,}\text{\hspace{0.17em}}\text{since}\text{\hspace{0.17em}}x=215,\text{\hspace{0.17em}}x+2=217.\hfill \end{array}$
$\begin{array}{ll}\text{Step}\text{\hspace{0.17em}}4:\hfill & 215+217=432,\text{\hspace{0.17em}}\text{but}\text{\hspace{0.17em}}215\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}217\text{\hspace{0.17em}}\text{are}\text{\hspace{0.17em}}\text{odd}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{we}\text{\hspace{0.17em}}\text{are}\text{\hspace{0.17em}}\text{looking}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}\text{even}\text{\hspace{0.17em}}\text{numbers}\text{.}\hfill \\ \hfill & \text{Upon}\text{\hspace{0.17em}}\text{checking}\text{\hspace{0.17em}}\text{our}\text{\hspace{0.17em}}\text{method}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{solution}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{reexamining}\text{\hspace{0.17em}}\text{our}\text{\hspace{0.17em}}\text{equation},\text{\hspace{0.17em}}\text{we}\text{\hspace{0.17em}}\text{find}\text{\hspace{0.17em}}\text{no}\hfill \\ \hfill & \text{mistakes}\text{.}\hfill \\ \text{Step}\text{\hspace{0.17em}}5:\hfill & \text{We}\text{\hspace{0.17em}}\text{must}\text{\hspace{0.17em}}\text{conclude}\text{\hspace{0.17em}}\text{that}\text{\hspace{0.17em}}\text{this}\text{\hspace{0.17em}}\text{problem}\text{\hspace{0.17em}}\text{has}\text{\hspace{0.17em}}\text{no}\text{\hspace{0.17em}}\text{solution}\text{.}\text{\hspace{0.17em}}\text{There}\text{\hspace{0.17em}}\text{are}\text{\hspace{0.17em}}\text{no}\text{\hspace{0.17em}}\text{two}\text{\hspace{0.17em}}\text{consecutive}\text{\hspace{0.17em}}even\hfill \\ \hfill & \text{numbers}\text{\hspace{0.17em}}\text{that}\text{\hspace{0.17em}}\text{sum}\text{\hspace{0.17em}}\text{to}\text{\hspace{0.17em}}\text{432}\text{.}\hfill \end{array}$

## Practice set e

The sum of two consecutive even numbers is 498. What are the two numbers?

The two numbers are 248 and 250.

## Exercises

Solve the following problems. Note that some of the problems may seem to have no practical applications and may not seem very interesting. They, along with the other problems, will, however, help to develop your logic and problem-solving ability.

If eighteen is subtracted from some number the result is fifty-two. What is the number?

1. Let $x=$
2. The equation is
3. (Solve the equation.)
4. (Check)
5. The number is .

Step 1: Let $x$ = the unknown quantity.

Step 2: The equation is $x-18=52.$

Step 3: (Solve the equation.) Add 18 to each side.

$x-18+18=52+18$

$x=70$

Step 4: (Check) $70-18=52;$ True.

Step 5: The number is 70.

If nine more than twice a number is forty-six, what is the number?

1. Let $x=$
2. The equation is
3. (Solve the equation.)
4. (Check)
5. The number is .

If nine less than three eighths of a number is two and one fourth, what is the number?

1. Let $x=$
2. The number is .

Step 5: The number is 30.

Twenty percent of a number is 68. What is the number?

1. Let $x=$
2. The number is .

Eight more than a quantity is 37. What is the original quantity?

1. Let $x=$
2. The original quantity is .

Step 5: The original quantity is 29.

If a quantity plus $85%$ more of the quantity is $62.9$ , what is the original quantity?

1. Let $x=$ original quantity.
2. $\begin{array}{cccc}\underset{\begin{array}{l}\text{original}\\ \text{quantity}\end{array}}{\underbrace{x}}& +& \underset{\begin{array}{l}\\ \text{85%}\text{\hspace{0.17em}}\text{more}\end{array}}{\underbrace{.85x}}& =62.9\end{array}$
3. The original quantity is .

A company must increase production by $12%$ over last year’s production. The new output will be 56 items. What was last year’s output?

1. Let $P=$
2. Last year’s output was items.

Step 5: Last year's output was 50 items.

A company has determined that it must increase production of a certain line of goods by $1\frac{1}{2}$ times last year’s production. The new output will be 2885 items. What was last year’s output?

1. Last year’s output was items.

A proton is about 1837 times as heavy as an electron. If an electron weighs $2.68$ units, how many units does a proton weigh?

1. A proton weighs units.

Step 5: A proton weighs $\text{4923}\text{.16}$ units.

Neptune is about 30 times as far from the sun as is the Earth. If it takes light 8 minutes to travel from the sun to the Earth, how many minutes does it take to travel to Neptune?

1. Light takes minutes to reach Neptune.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
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
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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?
what is a peer
What is meant by 'nano scale'?
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 ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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
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