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 ?
Answers
Answer:
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Step-by-step explanation:
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Given :-
Three consecutive integers are such that, when they are taken in increasing order and multiplied by 2, 3, and 4, respectively.
Sum of the integers = 74
To Find :-
The first integer.
The second integer.
The third integer.
Analysis :-
Consider the three consecutive numbers as variables according to the question.
Make an equation.
Solve the variable and substitute it in the other sides as well and get their values too.
Solution :-
Let the three consecutive integers are x, x+1 and x+2.
Given that,
Sum of the integers = 74
Making an equation,
2x + 3(x+1) + 4(x+2) = 74
2x + 3x +3 + 4x + 8 = 74
Taking the like terms,
2x + 3x + 4x + 3 + 8 = 74
9x + 11 = 74
By transposing,
9x = 74 - 11
9x = 63
Finding x,
x = 63/9
x = 7
The numbers are,
x = 7
x + 1 = 8
x + 2 = 9
Therefore, the numbers are 7, 8 and 9.