1. ALGEBRAIC WORD PROBLEMS

2. Problem 1:
A number exceeds another by 4 and their sum is 32. Find the two numbers. Rep: x 1st number x + 4 2nd number Equation: x + x + 4 = 32 2x + 4 = 32 2x = 32 – 4 2x = 28 x = 14 Statement: The two numbers are 14 and 18.

3. Problem 2:
When a number is doubled and 5 is subtracted from the result, the answer is 37. What is the number. Rep.: let x be the missing number Equation: 2x – 5 = 37 2x = x = 42 x = 21 Statement: The missing number is 21.

4. Problem 3:
The sum of two numbers is 120. If the larger number is four times the smaller number, what are the two numbers? Rep.: let x be the smaller number and 4x the bigger number Equation: x + 4x = 120 5x = 120 x = 24 Statement: The two numbers are 24 and 96.

5. Problem 4:
The sum of three consecutive even numbers is 210. Find the largest of these numbers. Rep.: let x, x + 2, and x + 4 be the numbers Equation: x + (x + 2) + (x + 4) = 210 3x + 6 = 210 3x = 210 – 6 3x = 204 x = 68 Statement: The largest number is 72.

6. Problem 5:
Find two consecutive odd numbers such that when the smaller number is subtracted from three times the bigger number, the result is 56. Rep.: let x and x + 2 be the numbers Equation: 3 (x + 2) – x = 56 3x + 6 – x = 56 2x = 56 – 6 2x = 50 x = 25 Statement: The two numbers are 25 and 27.

7. Problem 6:
Ahmad is twice as old as Bobby. John is 7 years younger than Ahmad. If the sum of their ages is 38, how old are the three boys?

8. Problem 7:
Ben is three times as old as Carl now. In two years’ time, Ben will be twice as old as Carl. How old is Carl now?

9. Problem 8:
The length of a rectangle is 7 cm longer than its width. If the perimeter of the rectangle is 74 cm, find the length and the area of the rectangle.