# 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.

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Almas
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yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
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William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
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revolt
da
Application of nanotechnology in medicine
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Kamaluddeen
yes
narayan
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Professor
I think
Professor
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Anam
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Anam
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brayan
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Damian
Eleven fifteenths of two more than a number is eight.
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