 Hi friends, I am Pooja and today we will work out the following question. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers. Let us begin with the solution now. Now let the three consecutive integers be x plus 1 and x plus 2. Now in the question we are given that these three integers are multiplied by 2, 3 and 4 respectively. So the integers when multiplied by 2, 3 and 4 respectively will give. So now when x is multiplied by 2, we get into 2 which is equal to 2x. When x plus 1 is multiplied by 3, we get x plus 1 into 3 which is equal to 3x plus 3 because 3 multiplied by x gives 3x plus 3 multiplied by 1 gives 3 and when x plus 2 is multiplied by 4, we get x plus 2 into 4 is equal to 4x plus 8 because 4 multiplied by x gives 4x plus 4 multiplied by 2 gives 8. So we get 4x plus 8. Now in the question we have that when these three integers are multiplied by 2, 3 and 4 respectively, they add up to 74. So according to the given condition, we have 2x plus 3x plus 3 plus 4x plus 8 is equal to 74. This implies now 2x plus 3x is equal to 5x and 5x plus 4x is equal to 9x. So we have 9x plus 3 plus 8 is equal to 11. So we have 11 is equal to 74. This implies 9x is equal to 74 minus 11 taking 11 to the right hand side of equal to sign, we get 9x is equal to 74 minus 11. This further implies 9x is equal to now 74 minus 11 is equal to 63. So we get 9x is equal to 63. Now dividing both the sides by 9 we get 9x upon 9 is equal to 63 upon 9. This further implies now cancelling out common factor 9. Here we get 1 enumerator and here cancelling out common factor 9 we get 7 enumerator. So we get x is equal to 7 because 1 into x is equal to x and this is equal to 7. So we have got the value of x as 7 thus we have the 3 consecutive integers are 7 and 9 because we have assumed the 3 consecutive integers to be x, x plus 1 and x plus 2 and we have got the value of x as 7. So the first integer becomes 7 then x plus 1 is equal to 7 plus 1 which is equal to 8. So the second integer is 8 and the third integer is 7 plus 2 which is equal to 9. Thus we write our answer as the 3 consecutive integers are 7, 8 and 9. Hope you have understood the solution. Bye and take care.