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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

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.

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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

0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply
tan20?×tan40?×tan80?
Santosh Reply
At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?
Kimberly Reply
-3 and -2
Julberte Reply
tan(?cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
Chirag Reply
tan(pi.cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
Chirag Reply
sin x(1+tan x)+cos x(1+cot x) = sec x +cosec
Ankit Reply
let p(x)xq
Sophie Reply
To the nearest whole number, what was the initial population in the culture?
Cheyenne Reply
do posible if one line is parallel
Fran Reply
The length is one inch more than the width, which is one inch more than the height. The volume is 268.125 cubic inches.
Vamprincess Reply
Using Earth’s time of 1 year and mean distance of 93 million miles, find the equation relating ?T??T? and ?a.?
James Reply
cos(x-45)°=Sin x ;x=?
Samaresh Reply
10-n ft
Nalin Reply
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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