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### Grade 7 - Mathematics6.16 Word Problems - Numbers

 Procedure: Read the problem carefully and note down what is given and what is required. Select a letter say x or y or z to represent the unknown quantity asked for. Represent the word statements of the problems in the symbolic language step by step. Look for quantities which are equal as per conditions given and form an equation. Solve the equation. Verify the result for making sure that your answer satisfies the requirements of the problems. Example: Half of a certain number added to its one third makes it 40. What is the number. Solution: Let the number be x. Half of the number = x/2 One third of the number = x/3 As per condition of the problem x/2 + x/3 = 40 ..........I L.C.M. of the denominators 2 and 3 is 6. Multiplying both sides of the equation by 6, we get (3x+2x)/6 = 40 5x/6 = 40 5x = 40 * 6 5x = 240 x = 240/5 x = 48 Verification: Substituting x = 48 in the equation I L.H.S. = x/2 + x/3 = 48/2 + 48/3 = 24 + 16 = 40 = R.H.S. Therefore x = 48 is the required number. Directions: Solve the following word problems. Also write at least ten examples of your own.
 Q 1: A number is multiplied by 3 and 6 is added to the product. If this sum is divided by 6 the result is equal to 8. Find the number.15141721 Q 2: If a number is tripled and 12 is added to it, the result is equal to 30. Find the number. (Hint: Let the number be x. The algebraic equation is 3x + 12 = 30, Solve for x)615712 Q 3: Divide 30 into two parts so that one part is twice that other part. (Hint: Let a be one part then the other part is 2a. The equation can be written as a + 2a = 30, find a and 2a)10 and 20 5 and 2515 and 1510 and 15 Q 4: One third of a certain quantity exceeds one seventh of that quantity by 12. Find the quantity. (Hint: a/3 - a/7 = 12 or a/3 = 12 - a/7, solve for a)1563573 Q 5: If a number is multiplied by 6 and 10 is subtracted from the product, the result is equal to 44. Find the number. (Hint: algebraic equation 6a - 10 = 44)9356 Q 6: 4 is subtracted from a number and the difference is multiplied by 2. If 15 is added to the product and the sum is divided by 7, the result is equal to 9. Find the number.38281856 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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