Lesson 12
Solving Problems with Algebra
Practice Exercise 12-2 Answer Key

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

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,  1 x = 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