2Problem Solving Day 1 Value Problems Math 8HProblem Solving Day 1Value ProblemsAlgebra Glencoe McGraw-Hill JoAnn Evans
3Five times a number, increased by 3, is the same as three times the number, increased by 27. Find the number.Let Statement:Let x = the numberVerbal Sentence:Five times a number, plus 3, equals three times the number, plus 27.Equation:5x + 3 = 3x + 27Solution:The number is 12.5x + 3 = 3x + 27-3x x2x + 3 = 272x = 24x = 12
4The sum of four consecutive ODD integers is -56. What are the integers? Let Statements:Let x = the first odd integerLet x + 2 = the second odd integerLet x + 4 = the third odd integerLet x + 6 = the fourth odd integerVerbal Sentence:First plus second plus third plus fourth equals total.Equation:x + (x + 2) + (x + 4) + (x + 6) = -56
5x + (x + 2) + (x + 4) + (x + 6) = -56 4x + 12 = -56 - 12 - 12 4x = -68 4x = -68x = -17(-17) + 2 = -15Once you’ve found x, refer to the Let Statements to name the other integers.(-17) + 4 = -13(-17) + 6 = -11Solution:The integers are-17, -15, -13, and -11.
6Two widths plus two lengths equals perimeter Equation: The length of a rectangle is seven more than three times the width. If the perimeter of the rectangle is 46 inches, what are the dimensions?Let Statements:Let x = widthLet 3x + 7 = the lengthVerbal Sentence:Two widths plus two lengths equals perimeterEquation:2x + 2(3x + 7) = 463x + 7xx3x + 7
7The width is 4 inches and the length is 19 inches. 2x + 2(3x + 7) = 462x + 6x = 468x = 468x = 32x = 4Solution:The width is 4 inches and the length is 19 inches.
8Let x = # of student tickets Adult tickets for the annual Teacher vs. Student softball game cost $4 each and student tickets went for $2 each. A total of 920 tickets were sold, bringing in $2446 for the school. How many student tickets were sold?Let Statements:Let x = # of student ticketsLet 920 – x = # of adult tickets (total – students)Verbal Sentence:Value student tickets + value adult tickets = total Value
9617 student tickets were sold. Equation:2x + 4(920 – x) = 24462x x = 2446-2x = 2446-2x = -1234x = 617Solution:617 student tickets were sold.
10Think of the value in cents to avoid decimals. Jessie has a wallet full of coins to spend, all either dimes or quarters. She has six times the number of dimes as she does quarters. If the total value of her coins is $9.35, how many of each coin does she have?Let Statements:Let x = # of quartersLet 6x = # of dimesVerbal Sentence:VALUE of quarters + VALUE of dimes = total ValueThink of the value in cents to avoid decimals.
11Jessie has 11 quarters and 66 dimes. Equation:25x (6x) = 93525x + 60x = 93585x = 935x = 11Solution:Jessie has 11 quarters and 66 dimes.
12Ryan has taken 3 algebra quizzes so far this year Ryan has taken 3 algebra quizzes so far this year. His score on the first quiz was 80. His score on the second quiz was five more than the first. What must his score be on the third quiz to raise his average to 88?Let Statement:Let x = score on 3rd quizVerbal Sentence:1st score + 2nd score + 3rd score3= new average
13Ryan needs a 99 on the 3rd quiz. Equation:1Solution:Ryan needs a 99 on the 3rd quiz.