# 2.3 Models and applications  (Page 4/9)

 Page 4 / 9

A game room has a perimeter of 70 ft. The length is five more than twice the width. How many ft 2 of new carpeting should be ordered?

250 ft 2

## Solving a volume problem

Find the dimensions of a shipping box given that the length is twice the width, the height is $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ inches, and the volume is 1,600 in. 3 .

The formula for the volume of a box is given as $\text{\hspace{0.17em}}V=LWH,$ the product of length, width, and height. We are given that $\text{\hspace{0.17em}}L=2W,$ and $\text{\hspace{0.17em}}H=8.\text{\hspace{0.17em}}$ The volume is $\text{\hspace{0.17em}}1,600\text{\hspace{0.17em}}$ cubic inches.

$\begin{array}{ccc}\hfill V& =& LWH\hfill \\ \hfill 1,600& =& \left(2W\right)W\left(8\right)\hfill \\ \hfill 1,600& =& 16{W}^{2}\hfill \\ \hfill 100& =& {W}^{2}\hfill \\ \hfill 10& =& W\hfill \end{array}$

The dimensions are $\text{\hspace{0.17em}}L=20\text{\hspace{0.17em}}$ in., $\text{\hspace{0.17em}}W=10\text{\hspace{0.17em}}$ in., and $\text{\hspace{0.17em}}H=8\text{\hspace{0.17em}}$ in.

Access these online resources for additional instruction and practice with models and applications of linear equations.

## Key concepts

• A linear equation can be used to solve for an unknown in a number problem. See [link] .
• Applications can be written as mathematical problems by identifying known quantities and assigning a variable to unknown quantities. See [link] .
• There are many known formulas that can be used to solve applications. Distance problems, for example, are solved using the $\text{\hspace{0.17em}}d=rt\text{\hspace{0.17em}}$ formula. See [link] .
• Many geometry problems are solved using the perimeter formula $\text{\hspace{0.17em}}P=2L+2W,$ the area formula $\text{\hspace{0.17em}}A=LW,$ or the volume formula $\text{\hspace{0.17em}}V=LWH.\text{\hspace{0.17em}}$ See [link] , [link] , and [link] .

## Verbal

To set up a model linear equation to fit real-world applications, what should always be the first step?

Answers may vary. Possible answers: We should define in words what our variable is representing. We should declare the variable. A heading.

Use your own words to describe this equation where n is a number:

$5\left(n+3\right)=2n$

If the total amount of money you had to invest was $2,000 and you deposit $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ amount in one investment, how can you represent the remaining amount? $2,000-x$ If a man sawed a 10-ft board into two sections and one section was $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ ft long, how long would the other section be in terms of $\text{\hspace{0.17em}}n$ ? If Bill was traveling $\text{\hspace{0.17em}}v\text{\hspace{0.17em}}$ mi/h, how would you represent Daemon’s speed if he was traveling 10 mi/h faster? $v+10$ ## Real-world applications For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113? Beth and Ann are joking that their combined ages equal Sam’s age. If Beth is twice Ann’s age and Sam is 69 yr old, what are Beth and Ann’s ages? Ann: $\text{\hspace{0.17em}}23;$ Beth: $\text{\hspace{0.17em}}46$ Ben originally filled out 8 more applications than Henry. Then each boy filled out 3 additional applications, bringing the total to 28. How many applications did each boy originally fill out? For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of$20 and charges of $.05/min for calls. Company B has a monthly fee of$5 and charges $.10/min for calls. #### Questions & Answers By the definition, is such that 0!=1.why? Unikpel Reply (1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin\$)
hatdog
Mark
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
bsc F. y algebra and trigonometry pepper 2
given that x= 3/5 find sin 3x
4
DB
remove any signs and collect terms of -2(8a-3b-c)
-16a+6b+2c
Will
is that a real answer
Joeval
(x2-2x+8)-4(x2-3x+5)
sorry
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
(X2-2X+8)-4(X2-3X+5)=0 ?
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
Y
master
X2-2X+8-4X2+12X-20=0 (X2-4X2)+(-2X+12X)+(-20+8)= 0 -3X2+10X-12=0 3X2-10X+12=0 Use quadratic formula To find the answer answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20 x2-4x2-2x+12x+8-20 -3x2+10x-12 now you can find the answer using quadratic
Mukhtar
2x²-6x+1=0
Ife
explain and give four example of hyperbolic function
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
y/y+10
Mr
Find nth derivative of eax sin (bx + c).
Find area common to the parabola y2 = 4ax and x2 = 4ay.
Anurag
y2=4ax= y=4ax/2. y=2ax
akash
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
thanks
Jhovie
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
A banana.
Yaona
a function
Daniel
a function
emmanuel
given 4cot thither +3=0and 0°<thither <180° use a sketch to determine the value of the following a)cos thither
what are you up to?
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda