
Concept explainers
To find: the amount money Hilary, Paul and Jeff have

Answer to Problem 4ST
The amount of money Hilary have is
The amount of money Paul have is
The amount of money Jeff have is
Explanation of Solution
Given information: “Hilary has three times as much money as Paul”, “Jeff has $4 less than Hilary and $5 more than Paul”
Concept Involved:
Assign variable for the unknown that we need to find. Use the keywords in the statement to rewrite the statement to meaningful math equation.
“same as” means =
“more than” means +
“less” means −
Solve the equation by getting the variable in one side of the equation and undoing whatever is done to it by performing reverse operation.
Calculation: Let ‘ x’ be the amount of money Paul have
Using the keywords given in the sentence “Hilary has three times as much money as Paul” we can conclude that the amount of money Hilary have is ‘ 3x’
Using the keywords given in the sentence “Jeff has $4 less than Hilary and $5 more than Paul” we can get two expressions to represent the amount of money Jeff have as ‘ 3x-4’ & ‘ x+5’
We can equate the two expressions representing Jeff money
In the process of getting x in one side of the equation subtract on both sides
Combine like terms on both sides
Add 4 on both sides of the equation
Divide by 3 on both sides of the equation
Simplify fraction on both sides of the equation
Evaluate the value of the expression 3x by substituting 4.5 for x
Evaluate the value of the expression
Conclusion:
The amount of money Hilary is represented by expression
The amount of money Paul is represented by expression x and equal to
The amount of money Jeff is represented by expression
Chapter 3 Solutions
Algebra: Structure And Method, Book 1
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Introductory Statistics
A First Course in Probability (10th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Thinking Mathematically (6th Edition)
College Algebra (7th Edition)
- Practice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forwardAnswer the questionsarrow_forwardHow can I prepare for me Unit 3 test in algebra 1? I am in 9th grade.arrow_forward
- Asked this question and got a wrong answer previously: Third, show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say?arrow_forwardDetermine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.arrow_forwardThe 173 acellus.com StudentFunctions inter ooks 24-25/08 R Mastery Connect ac ?ClassiD-952638111# Introduction - Surface Area of Composite Figures 3 cm 3 cm 8 cm 8 cm Find the surface area of the composite figure. 2 SA = [?] cm² 7 cm REMEMBER! Exclude areas where complex shapes touch. 7 cm 12 cm 10 cm might ©2003-2025 International Academy of Science. All Rights Reserved. Enterarrow_forward
- You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methodsarrow_forwardPlane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)arrow_forwardshow that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education





