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There are $3$ consecutive integers that have a sum of $45$ . Which integers are they? $\newline$ $\_$ , $\_$ , $\_$

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Consecutive integer problems

Full solution

Q. There are

3

consecutive integers that have a sum of

45

. Which integers are they?

\newline

\_

,

\_

,

\_

Identify First Integer: Let $x$ be the first integer. $\newline$ Which represents the three consecutive integers? $\newline$ Consecutive integers increase by $1$ each time. $\newline$ Consecutive integers: $x$ , $x+1$ , $x+2$
Sum of Consecutive Integers: Which equation represents the sum of $3$ consecutive integers is $45$ ? $\newline$ Add three consecutive integers and equate the sum to $45$ . $\newline$ Equation: $x + (x+1) + (x+2) = 45$
Simplify Equation: Simplify the left side of $x + (x+1) + (x+2) = 45$ . $\newline$ $x + (x+1) + (x+2) = 45$ $\newline$ $(x + x + x) + (1+2) = 45$ $\newline$ $3x + 3 = 45$
Isolate Variable Term: Isolate the variable term in $3x + 3 = 45$ .
$3x + 3 = 45$
$3x + 3 - 3 = 45 - 3$
$3x = 42$
Solve for x: $3x = 42$ $\newline$ Solve for x. $\newline$ $3x = 42$ $\newline$ $(3x)/3 = 42/3$ $\newline$ $x = 14$
Final Consecutive Integers: We have: $\newline$ $x = 14$ $\newline$ What are the $3$ consecutive integers that add up to $45$ ? $\newline$ Three consecutive integers: $\newline$ $x, x+1, x+2$ $\newline$ $14, 14+1, 14+2$ $\newline$ $14, 15, 16$

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