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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

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Solving a volume problem

Find the dimensions of a shipping box given that the length is twice the width, the height is 8 inches, and the volume is 1,600 in. 3 .

The formula for the volume of a box is given as V = L W H , the product of length, width, and height. We are given that L = 2 W , and H = 8. The volume is 1,600 cubic inches.

V = L W H 1 , 600 = ( 2 W ) W ( 8 ) 1 , 600 = 16 W 2 100 = W 2 10 = W

The dimensions are L = 20 in., W = 10 in., and H = 8 in.

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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 d = r t formula. See [link] .
  • Many geometry problems are solved using the perimeter formula P = 2 L + 2 W , the area formula A = L W , or the volume formula V = L W H . See [link] , [link] , and [link] .

Section exercises


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.

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

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5 ( n + 3 ) = 2 n

If the total amount of money you had to invest was $2,000 and you deposit x amount in one investment, how can you represent the remaining amount?

2 , 000 x

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If a man sawed a 10-ft board into two sections and one section was n ft long, how long would the other section be in terms of n ?

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If Bill was traveling v mi/h, how would you represent Daemon’s speed if he was traveling 10 mi/h faster?

v + 10

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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?

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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: 23 ; Beth: 46

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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?

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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

answer and questions in exercise 11.2 sums
Yp Reply
how do u calculate inequality of irrational number?
give me an example
and I will walk you through it
cos (-z)= cos z .
what is a algebra
Jallah Reply
what is the identity of 1-cos²5x equal to?
liyemaikhaya Reply
__john __05
C'est comment
h r u friends
so is their any Genius in mathematics here let chat guys and get to know each other's
I speak French
okay no problem since we gather here and get to know each other
hi im stupid at math and just wanna join here
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
it's 12
what is the function of sine with respect of cosine , graphically
Karl Reply
tangent bruh
Aashish Reply
sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
 Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
each term in a sequence below is five times the previous term what is the eighth term in the sequence
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
sinx sin2x is linearly dependent
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
Aasik Reply
Wrong question
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
2x + 7 =19
2x +7=19. 2x=19 - 7 2x=12 x=6
because x is 6
Practice Key Terms 3

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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