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Math 8H Problem Solving Day 1 Value Problems Algebra 1 Glencoe McGraw-Hill JoAnn Evans

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Five 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 number Verbal Sentence: Five times a number, plus 3, equals three times the number, plus 27. Equation: 5x + 3 = 3x + 27 Solution: The number is 12. 5x + 3 = 3x + 27 -3x 2x + 3 = 27 - 3 2x = 24 x = 12

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The sum of four consecutive ODD integers is -56. What are the integers? Let Statements: Let x = the first odd integer Let x + 2 = the second odd integer Let x + 4 = the third odd integer Let x + 6 = the fourth odd integer Verbal Sentence: First plus second plus third plus fourth equals total. Equation: x + (x + 2) + (x + 4) + (x + 6) = -56

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4x + 12 = -56 - 12 - 12 4x = -68 x = -17 Once you’ve found x, refer to the Let Statements to name the other integers. (-17) + 2 = -15 (-17) + 4 = -13 (-17) + 6 = -11 Solution: The integers are -17, -15, -13, and -11.

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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 = width Let 3x + 7 = the length Verbal Sentence: Two widths plus two lengths equals perimeter Equation: 2x + 2(3x + 7) = 46 3x + 7 xx

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Solution: 2x + 2(3x + 7) = 46 2x + 6x + 14 = 46 8x + 14 = 46 - 14 - 14 8x = 32 x = 4 The width is 4 inches and the length is 19 inches.

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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 tickets Let 920 – x = # of adult tickets (total – students) Verbal Sentence: Value student tickets + value adult tickets = total Value

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Solution: 2x + 4(920 – x) = 2446 Equation: 2x + 3680 - 4x = 2446 -2x + 3680 = 2446 - 3680 -3680 -2x = -1234 x = 617 617 student tickets were sold.

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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 quarters Let 6x = # of dimes Verbal Sentence: VALUE of quarters + VALUE of dimes = total Value Think of the value in cents to avoid decimals.

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Equation: Solution: 25x + 60x = 935 85x = 935 x = 11 Jessie has 11 quarters and 66 dimes. 25x + 10(6x) = 935

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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 3 rd quiz Verbal Sentence: 1 st score + 2 nd score + 3 rd score 3 = new average

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Equation: Solution: Ryan needs a 99 on the 3 rd quiz. 1

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