THREE CONSECUTIVE INTEGERS ARE SUCH THAT ARE TAKEN IN INCREASING ORDER AND MULTIPLEX BY 2,3 AND 4 RESPECTIVELY, THEY ADD UP TO 74.FIND THESE NUMBERS
Answers
Step-by-step explanation:
Given :-
Three consecutive integers are such that taken in increasing order and multiplied by 2 , 3 and 4 respectively and they add up to 74.
To find :-
Fond the numbers ?
Solution :-
Let the consecutive integers be X , X+1 and X+2
They are taken in the Increasing order
X < X+1 < X+2
On multiplying X with 2 then the result
= 2× X
= 2X -----------(1)
On multiplying X+1 with 3 then the result
= 3×(X+1)
= 3X+3 ---------(2)
On multiplying with X+2 with 4 then the result
= 4×(X+2)
=4X+8 ---------(3)
On adding (1) ,(2) & (3)
= 2X + 3X+3 + 4X+8
= (2X+3X+4X) +(3+8)
= 9X + 11 --------(4)
According to the given problem
Their sum after multiplying them with 2 , 3 and 4 respectively = 74--------(5)
(4) and (5) are equal.
=> 9X + 11 = 74
=> 9X = 74 - 11
=> 9X = 63
=> X = 63 / 9
=> X = 7
Therefore, X = 7
X+1 = 7+1 = 8
X+2 = 7+2 = 9
Therefore, The numbers are 7,8 and 9
Answer :-
The required three consecutive integers are 7,8 and 9
Check:-
The numbers are 7,8 and 9
7< 8< 9
On multiplying 7 with 2 the result
= 7×2 = 14
On multiplying 8 with 3 the result
= 8×3 = 24
On multiplying 9 with 4 the result
= 9×4 = 36
Thier sum = 14+24+36 = 74
Verified the given relations in the given problem.