Find the three consecutive odd numbers such that their sum is equal to 147
ANSWER
Verified
Hint: Assume the three consecutive odd numbers by using (2n + 1) as general form and then add them and equate them with 147 so that you can get the value of the variable you have assumed. Then put the value of the variable in assumed numbers to get the final answer.
Complete step-by-step solution - To solve the problem given above we should assume the three numbers first, As it is mentioned in the question that the three consecutive numbers are odd therefore we will assume them as follows, (2x + 1), (2x + 3) and (2x + 5) ……………………………………………………….. (1) As we have given that the summation of three consecutive odd numbers is equal to 147 therefore we will add the assumed numbers from equation (1) and equate them with 147, therefore we will get, (2x + 1) + (2x + 3) + (2x + 5) = 147 If we open the brackets from the above equation we will get, 2x + 1 + 2x + 3 + 2x + 5 = 147 By rearranging the above equation we will get, 2x + 2x + 2x +1 + 3 + 5 = 147 By performing addition operation in the above equation we will get, 6x + 9 = 147 By shifting 9 on the right hand side of the equation we will get, 6x = 147 – 9 By simplifying the above equation we will get, 6x = 138 Now, if we shift 6 on the right hand side of the equation we will get, $x=\dfrac{138}{6}$ By simplifying the above equation we will get, x = 23 If we put x = 23 in equation (1) we will get the numbers as, \[\left( 2\times 23+1 \right),\left( 2\times 23+3 \right)\] and \[\left( 2\times 23+5 \right)\] Therefore we will get the numbers as, \[\left( 46+1 \right),\left( 46+3 \right)\] and \[\left( 46+5 \right)\] Therefore, The three consecutive odd numbers are 47, 49 and 51 respectively.
Note: Alternate Solution -> Whenever you get a question with sum of certain consecutive numbers, take them as (a-d), a, (a+d), etc. such that their addition cancels the second variable. For example, in this question, the numbers were (a-2), a, (a+2).
Their sum is (a-2) + a + (a+2) = 3a = 147
Means, a = 49.
So the three numbers are 47, 49 and 51
Similarly if it were a question of multiplication, you should assume the numbers as a/d, a, ad and so on...