The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling? A. 17 B. 18 C. 19 D. 21 E. 22 The OA is the option A. Experts, how can determine the age of the youngest sibling without knowing any of their ages?

Vincen wrote:The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling? A. 17 B. 18 C. 19 D. 21 E. 22 Let y = the age of the youngest child So, y + 3 = age of sibling who is 3 years older than the youngest child y + 5 = age of sibling who is 5 years older than the youngest child y + 8 = age of sibling who is 8 years older than the youngest child The average (arithmetic mean) age of the 4 siblings is 21 This means: [y + (y+3) + (y+5) + (y+8)]/4 = 21 Multiply both sides by 4 to get: y + (y+3) + (y+5) + (y+8) = 84 Simplify: 4y + 16 = 84 Solve: y = 17 Answer: A Cheers, Brent

Vincen wrote:The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling? A. 17 B. 18 C. 19 D. 21 E. 22 The OA is the option A. Experts, how can determine the age of the youngest sibling without knowing any of their ages? We can let x = the age of the youngest child; thus, the ages of the three older children are x + 3, x + 5 and x + 8, respectively. We can create the equation: (x + x + 3 + x + 5 + x + 8)/4 = 21 4x + 16 = 84 4x = 68 x = 17 Answer: A

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