Answer:
14 , 15 , 16
Explanation:
"Consecutive" by definition means, quote "in unbroken or logical sequence". This means that, in the case of three numbers, the least number will be denoted by the variable, x, while the following "consecutive" numbers would be 1 greater than the last, making the terms 'x + 1' & 'x + 2'.
Set the equation:
x + (x + 1) + (x + 2) = 45
First, combine like terms. Like terms are terms with the same amount of the same variables:
(x + x + x) + (1 + 2) = 45
3x + 3 = 45
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis , Exponents (& Roots), Multiplications, Divisions, Additions, Subtractions.
First, subtract:
3x + 3 (-3) = 45 (-3)
3x = 45 - 3
3x = 42
Next, divide 3 from both sides of the equation:
(3x)/3 = (42)/3
x = 42/3
x = 14
Next, find the next three terms:
x = 14
x + 1 = 15
x + 2 = 16
Check: 14 + 15 + 16 = 45 (True).
Therefore, the 3 numbers is 14, 15, 16.
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