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Xin is the oldest of four siblings whose ages are consecutive integers. If the sum of their ages is 78, find Xin's age. Answer:

Xin is the oldest of four siblings whose ages are consecutive integers. If the sum of their ages is 7878, find Xin's age.\newlineAnswer:

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Full solution

Q. Xin is the oldest of four siblings whose ages are consecutive integers. If the sum of their ages is 7878, find Xin's age.\newlineAnswer:
  1. Denote Xin's age: Let's denote Xin's age as XX. Since the siblings have consecutive ages, the other three siblings' ages would be X−1X-1, X−2X-2, and X−3X-3. We are given that the sum of their ages is 7878. The equation representing the sum of their ages is: X+(X−1)+(X−2)+(X−3)=78X + (X - 1) + (X - 2) + (X - 3) = 78
  2. Simplify and solve: Now, let's simplify and solve the equation:\newline4X−6=784X - 6 = 78\newlineAdd 66 to both sides to isolate the term with X:\newline4X=78+64X = 78 + 6\newline4X=844X = 84
  3. Divide and calculate: Next, we divide both sides by 44 to solve for XX:X=844X = \frac{84}{4}X=21X = 21
  4. Final result: Xin's age, being the oldest, is the value of XX we just calculated, which is 2121 years old.

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