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

Directions: Compare your answers to Problems 12-2 with those in the Answer Key below.  If you get less than 8 items correct, please review the instruction.

1. The larger of two numbers is seven more than five times the other. Their sum is 55. Find the two numbers.
    
   Let x = the smaller number; then 5x + 7 = the larger number. Then your equation is: x + 5x + 7 = 55. And so the smaller number (x) = 8, and the larger number (5x + 7) = 47.
    
2. Separate 43 into two parts. The first part is five less than three times the second part. Find each part. 
    
   Let x = the second part. Then, the first part is 3x - 5. And so your equation is x + 3x - 5 = 43. So, the second part (x) = 12, and the first part (3x - 5) = 31.
    
3. In a game, Harry's score was three times Ben's score. Together, they scored 80 points. Find each score. 
    
   Let x = Ben's score, and let 3x = Harry's score. Then your equation is x + 3x = 80. And so Ben's score (x) = 20, and Harry's score (3x) = 60.
   
4. The sum of four consecutive numbers is 606. Find the numbers. 
    
   Let the 1st number = x, the 2nd number = x + 1, the 3rd number =  x + 3, and the 4th number = x + 4. Then your equation is x + x + 1 + x + 2 + x + 3 + x + 4 = 606. And so the numbers are: 150, 151, 152, and 153.
    
5. Abel, Bob and Carl are friends. Their ages add up to 49 years. Abel is eight years younger than Bob, and Carl is three years older than Bob. What are their ages? 
    
   Let Bob's age = x. Then Abel is x - 8, and Carl is x + 3. So your equation is x + x - 8 + x + 3 = 49. So Bob (x) = 18, and Abel (x - 8) = 10, and Carl (x + 3) = 21.
    
6. Roy is twice as old as Verna. In four years, he will be eight years older than she is. Find the age of each. 
    
   Let Verna's age = x, and then Roy's age is 2x. So, in four years Verna will be x + 4, and Roy will be 2x + 4. So your equation is 2x + 4 = x + 4 + 8. And so Verna is (x) = 8, and Roy (2x) = 16.
    
7. Steve is 16 years older than Denise. In three years, the sum of their ages will be 32. What is the age of each now? 
    
   Let x = the age of Denise, then x + 16 = Steve's age now. The your equation is x + 3 + x + 16 + 3 = 32. And so Denise is (x) = 5, and Steve is (x + 16) = 21.
    
8. One three ring binder costs twenty cents less than twice the cost of another. If ten of each of the binders costs $58.00, what is the price of each binder? 
    
   Let x = the price of one binder. Then 2x - .20 = the price of the other binder. Your equation then is 10x + 10(x - .20) = $58.00, and so the cost of first binder (x) = $2.00 and the second binder (2x -.20) = $3.80.
    
9. One computer printer can print three times as many lines per minute as another. If the total output of both printers is 1200 lines per minute, what is the print rate of each printer?
    
   Let x = the rate of the slowest printer. Then 3x = the rate of the fastest printer. Your equation is x + 3x = 1200; and so the rate of the slowest printer (x) = 300, and the rate of the fastest printer is (3x) = 900.
    
10. George's weekly salary is $200 less than twice John's weekly salary. If together they earn $700 per week, what is the weekly salary of each? 
     
    Let x = John's salary, and let 2x - $200 = George's salary. Your equation is: x + 2x - $200 = $700, and so John's weekly salary is (x) = $300, and George's weekly salary is (2x - $200) = $400.