1. Warm Up

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

3. 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 x
2x + 3 = 27
2x = 24
x = 12

4. 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

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

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

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

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

9. 617 student tickets were sold.
Equation:
2x + 4(920 – x) = 2446
2x x = 2446
-2x = 2446
-2x = -1234
x = 617
Solution:
617 student tickets were sold.

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

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

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

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