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Yasmin is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 126, find Yasmin's age. Answer:

Yasmin is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 126126, find Yasmin's age.\newlineAnswer:

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Full solution

Q. Yasmin is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 126126, find Yasmin's age.\newlineAnswer:
  1. Denote Yasmin's Age: Let's denote Yasmin's age as yy years. Since the siblings have consecutive ages, the other three siblings would be y+1y+1, y+2y+2, and y+3y+3 years old. We are given that the sum of their ages is 126126 years.\newlineThe equation representing the sum of their ages is:\newliney+(y+1)+(y+2)+(y+3)=126y + (y + 1) + (y + 2) + (y + 3) = 126
  2. Combine Like Terms: Now, let's combine like terms to simplify the equation: 4y+6=1264y + 6 = 126
  3. Subtract to Isolate: Next, we subtract 66 from both sides of the equation to isolate the terms with yy: \newline4y+6−6=126−64y + 6 - 6 = 126 - 6\newline4y=1204y = 120
  4. Divide to Solve: Now, we divide both sides of the equation by 44 to solve for yy: \newline4y4=1204\frac{4y}{4} = \frac{120}{4}\newliney=30y = 30
  5. Final Age Calculation: Since yy represents Yasmin's age, and we have found yy to be 3030, Yasmin is 3030 years old.

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