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There are $3$ consecutive integers with a sum of $51$ . What are the integers? $\newline$ $\_\_\_\_\_$ , $\_\_\_\_\_$ , $\_\_\_\_\_$

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Consecutive integer problems

Full solution

Q. There are

3

consecutive integers with a sum of

51

. What are the integers?

\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 $51$ ? $\newline$ Add three consecutive integers and equate the sum to $51$ . $\newline$ Equation: $x + (x+1) + (x+2) = 51$
Simplify Equation: Simplify the left side of $x + (x+1) + (x+2) = 51$ . $\newline$ $x + (x+1) + (x+2) = 51$ $\newline$ $(x + x + x) + (1+2) = 51$ $\newline$ $3x + 3 = 51$
Isolate Variable Term: Isolate the variable term in $3x + 3 = 51$ .
$3x + 3 = 51$
$3x + 3 - 3 = 51 - 3$
$3x = 48$
Solve for x: $3x = 48$ $\newline$ Solve for x. $\newline$ $3x = 48$ $\newline$ $(3x)/3 = 48/3$ $\newline$ $x = 16$
Final Consecutive Integers: We have: $\newline$ $x = 16$ $\newline$ What are the $3$ consecutive integers that add up to $51$ ? $\newline$ Three consecutive integers: $\newline$ $x, x+1, x+2$ $\newline$ $16, 16+1, 16+2$ $\newline$ $16, 17, 18$

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