Practice Exercise  12-2  (click HERE for a printer-friendly version)

Directions: Change the "Word Sentences" into Math Expressions or Equations when possible.  Consult the  Answer Key 12-2 below for answers once you finish. Review the Instruction material which relates to any questions you do not get correct.

1. The larger of two numbers is 6 less than 7 times the smaller and their sum is 74. What are the two numbers? = _____
    
2. Separate 90 into two parts, so that the second part is 30 less than twice the first part. Find each part. = _____
    
3. Joe's salary is four times Bob's salary. Together they earn $600. Find the salary of each man. = _____
    
4. The sum of three consecutive numbers (like 1, 2, 3) is 456. Find the three numbers. = _____
    
5. Five more than one-fourth of a number is two-thirds of that number. Find the number.  = _____
    
6. John, Bob, and Jim are brothers. The sum of their ages is 39 years. John is four years younger than Bob, and Jim is seven years older. How old is each?  = _____
    
7. Aaron is three times Betty's age. In six years, he will be twice her age. How old is each now?  = _____
    
8. Irv is eight years younger than June. Two years ago, she was three times older than he was. How old is each now?  = _____
    
9. Three tanks hold a total of 2200 gallons of water. The largest tank holds three times as much as the smallest, and twice as much as the other tank. How much water can each tank hold?  = _____
    
10. A 16-foot two-by-four piece of lumber is cut into two pieces so that one piece is three times as long as the other. How long is each piece?  = _____

Also, for more exercises go to: www.algebrahelp.com/lessons/equationbasics/pgw.htm for their Equation Basics Worksheet and read the instructions and do the exercises that follow.  After answering a question click on the question number for a step by step solution to the problem.

For more practice on problem solving go to:
http://www.accessone.com/~bbunge/Algebra/Algebra1-1.html.

Answer Key 12-2  (click HERE for a printer-friendly version) (top)

If you get less than 8 items correct, please review the instruction.

Click HERE if you have problems with any of the answers.

1. The larger of two numbers is 6 less than 7 times the smaller and their sum is 74. What are the two numbers?
   
   Let x = the smaller number;  7x - 6 = the larger number.
   x + 7x - 6 = 74
   8x = 80
   x = 10; 7x - 6 = 64
   
   
2. Separate 90 into two parts, so that the second part is 30 less than twice the first part.  Find each part.
   
   Let x = the smaller number;  2x - 30 = the larger number.
   x + 2x - 30 = 90
   3x = 120
   x = 40;  2x - 30 = 50
   
   
3. Joe's salary is four times Bob's salary.  Together they earn $600.  Find the salary of each man.
   
   Let x = Bob's salary;  4x = Joe's salary
   x + 4x = 5x = 600
   x = $120;  4x = $480
   
   
4. The sum of three consecutive numbers (like 1, 2, 3) is 456. Find the three numbers.
   
   Let x = first number;  x + 1 = the second number;  x + 2 = the third number
   3x + 3 = 456;  3x = 453;  x = 151
   The numbers are 151, 152, 153
   
   
5. Five more than one-fourth of a number is two-thirds of that number.  Find the number.
   
   Let x = the number.  x + 5 = x;  multiply by 12
   3x + 60 = 8x;  5x = 60;  x = 12.
   
   
6. John, Bob and Jim are brothers.  The sum of their ages is 39 years. John is four years younger than Bob, and Jim is seven years older.  How old is each?
   
   Let x = Bob's age;  x - 4 = John's age;  x + 7 = Jim's age
   x + x - 4 + x + 7 = 39;  3x = 36;  x = 12
   Their three ages are 12, 8, and 19.  
   
   
7. Aaron is three times Betty's age.  In six years he will be twice her age.  How old is each now?
   
   Let x = Betty's age now and x + 6 her age in 6 years;  3x = Aaron's age now and 3x + 6 his age in 6 years.  3x + 6 = 2(x + 6);
   3x + 6 = 2x + 12;  x = 6;  3x = 18;  Their ages = 6, and 18.
   
   
8. Irv is eight years younger than June.  Two years ago, she was three times older than he was.  How old is each now?
   
   Let x = June's age now and x - 2 her age 2 years ago;  x - 8 = Irv's age now and x -10 his age 2 years ago;
   x - 2 = 3(x - 10);  x - 2 = 3x - 30;  2x = 28;  x = 14
   June is 14 and Irv = x - 8 = 6.
    
9. Three tanks hold a total of 2200 gallons of water.  The largest tank holds three times as much as the smallest, and twice as much as the other tank.  How much water can each tank hold?
   Let x = size of smallest,  1x = size of next and 3x = size of largest
   Then x + 1x + 3x = 2200;  5x = 2200;  x = 400.
   The three tanks hold 400, 600, and 1200 gallons.
   
   
10. A sixteen-foot two-by-four piece of lumber is cut into two pieces so that one piece is three times as long as the other. How long is each piece? 
    
    Let x = the smaller and 3x the larger piece.
    4x = 16;  x = 4.  The two pieces are 4 and 12 feet