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Adriel is the youngest of four siblings whose ages are consecutive odd integers. If the sum of their ages is 120 , find Adriel's age.
Answer:

Adriel is the youngest of four siblings whose ages are consecutive odd integers. If the sum of their ages is $120$ , find Adriel's age. $\newline$ Answer:

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Partial sums of geometric series

Full solution

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

120

, find Adriel's age.

\newline

Answer:

Denote Adriel's age: Let's denote Adriel's age as $A$ . Since the siblings have consecutive odd ages, the ages of the other three siblings would be $A+2$ , $A+4$ , and $A+6$ respectively. We are given that the sum of their ages is $120$ . The equation representing the sum of their ages is: $A + (A + 2) + (A + 4) + (A + 6) = 120$
Simplify the equation: Now, let's combine like terms to simplify the equation: $4A + 12 = 120$
Subtract to solve: Next, we subtract $12$ from both sides of the equation to solve for $4A$ : $\newline$ $4A = 120 - 12$ $\newline$ $4A = 108$
Divide to find $A$ : Now, we divide both sides by $4$ to find $A$ : $A = \frac{108}{4}$ $A = 27$
Calculate Adriel's age: Since $A$ represents Adriel's age and we have calculated it to be $27$ , we have found Adriel's age.

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