Linear word problem based on number1

1. Linear word problem based on number1

2. Introduction What is an equation? An equation is a condition on the variable.An equation is a mathematical statement that shows that 2 quantities are equal. • 12 – 3 = 9Numerical • 3a = 30 Algebraic

3. Applications of Simple Equations to Practical Situation We can take statements from everyday language and convert them into simple equations. As we already know how to solve a simple equation, therefore we can easily solve puzzles/ problems from practical solutions. The method is first to form equations corresponding to such situations and then to solve those equations to give the solution to the puzzles/problems. Let us form Equations for Word statements and Solve by Adding/ Subtracting/ Multiplying/Dividing step and find the Unknown.

4. Solving Linear Equations Word Problems having Numbers • Consecutive positive integers are integers that follow each other in order. They • have a difference of 1 between each numbers. • Here, in number line 1, 2, 3, 4,5 are consecutive positive integers. 1 2 4 5 3 1 1 1 + 1 1 + 1 + 1 1 + 1 + 1 +1 1 + 1 + 1 +1+1 For Integer 1 1 1 1 + 1 1 + 2 1 + 3 1 + 4 For Integer ‘x’ x + 4 x x + 1 x + 2 x + 3 Firstnumber Second number Third number Fourth number Fifth number • For any integer ‘x’ the consecutive positive integers are x+1, x+2, x+3, x+4, etc.

5. 3 consecutive positive integers are a, a+1, a+ 2 Step 1: Writing Equation a + a + 1 +a +2 = 93 Group Variables 3a + 3 = 93 Step 2: Solve Transpose +3 to -3 3a = 93 – 3; 3a = 90 Divide both sides by 3 Example 1: Sum of 3 consecutive positive integers is 93. Find the third number if the first number is ‘a'. Solution: Break the statements and interpret. First number = 30 a = 30 Contd..

6. Contd.. Step 3: Find the 3rd number when 1st number a = 30 The 3 numbers are 30, 31, 32. From question, we need to write the 3rd number. 3rd Number = 32 Ans: The third number is 32.

7. Example 2: There are total 80 red and blue pens in a box. If number of red pens is 17 more than twice the number of blue pens, then find the number of red pens. Number of blue pens is ‘b’. Solution: Break the statements and Interpret. Step 1: Writing Equation: b + 2b + 17 = 80 Step 2: Solve 3b + 17 = 80 Transpose +17 to RHS 3b = 80 – 17; 3b = 63 Divide both sides by 3 Number of Blue pens = 21 Answer: Number of red pens are 59. Totally there are 80 pens b = 21

8. Contd.. Step 3: Find the number of red pens, when blue pens = 21 Substitute value of ‘b’ in 2b + 17 when b = 21 Number of Blue pens = 21; Number of Red pens = 59 Ans: Number of Red pens = 59

9. Example 3: Mother gave John and Jasmine some amount. John got Rs. 24 more than thrice the amount Jasmine got. If the total amount given was Rs.192, find the amount received by John. Let the amount got by Jasmine is rupees ‘a’. Solution: Break the statements and interpret. Step 1: Writing Equation : a + 3a + 24 = 192 Group Variables 4a + 24 = 192 Step 2: Solve Transpose +24 to RHS 4a = 192 – 24 Divide both sides by 4 4a = 168 a = 42 Amount got by Jasmine = Rs. 42 Contd..

10. Contd.. Jasmine got Rs. 42. Step 3: Find the amount received by John, when Jasmine got Rs. 42. Substitute value of ‘a’ in 3a + 24, when a = 42 3*(42) + 24 126 + 24 = 150 Ans: Amount received by John = Rs. 150

11. Try These Lily has 12 kg more than twice the amount James has. Total weight of oranges with both of them is 72 kg. Find the weight of oranges Lily has. Sum of 3 consecutive positive integers is 333. Find the third number. There are total 750 students in a school. Number of boys is 110 more than thrice the number of girls. Find the number of boys