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Jevonte is the oldest of four siblings whose ages are consecutive odd integers. If the sum of their ages is 128 , find Jevonte's age.
Answer:

Jevonte is the oldest of four siblings whose ages are consecutive odd integers. If the sum of their ages is $128$ , find Jevonte's age. $\newline$ Answer:

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Consecutive integer problems

Full solution

Q. Jevonte is the oldest of four siblings whose ages are consecutive odd integers. If the sum of their ages is

128

, find Jevonte's age.

\newline

Answer:

Identify Youngest Sibling's Age: Let $x$ be the age of the youngest sibling. $\newline$ Which represents the four consecutive odd integers? $\newline$ Consecutive odd integers increase by $2$ each time. $\newline$ Consecutive odd integers: $x$ , $x+2$ , $x+4$ , $x+6$
Find Consecutive Odd Integers: Which equation represents the sum of $4$ consecutive odd integers is $128$ ? $\newline$ Add four consecutive odd integers and equate the sum to $128$ . $\newline$ Equation: $x + (x+2) + (x+4) + (x+6) = 128$
Set Up Equation for Sum: Simplify the left side of $x + (x+2) + (x+4) + (x+6) = 128$ . $\newline$ $x + (x+2) + (x+4) + (x+6) = 128$ $\newline$ $(x + x + x + x) + (2+4+6) = 128$ $\newline$ $4x + 12 = 128$
Simplify Equation: Isolate the variable term in $4x + 12 = 128$ .
$4x + 12 = 128$
$4x + 12 - 12 = 128 - 12$
$4x = 116$
Isolate Variable Term: $4x = 116$ $\newline$ Solve for $x$ . $\newline$ $4x = 116$ $\newline$ $(4x)/4 = 116/4$ $\newline$ $x = 29$
Solve for x: We have: $\newline$ $x = 29$ $\newline$ What is Jevonte's age if he is the oldest sibling? $\newline$ Jevonte's age as the oldest sibling: $x + 6$ $\newline$ $29 + 6 = 35$

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