A girl is the eldest of 15 children and each child is exactly a year and a half apart.
Their ages form an arithmetic sequence with n=15 terms and common
difference d=1.5. So we use the formula:
an = a1 + (n-1)d
a15 = a1 + (15-1)(1.5)
a15 = a1 + (14)(1.5)
a15 = a1 + 21
The eldest is eight times the youngest age
The eldest's age is a15
The youngest's age is a1
So we have the system of two equations in two unknowns:
Solve by substitution or elimination and get
a1 = 3 and a15 = 24
The youngest is 3 and the eldest is 24
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Checking:
Their ages are
3, 4.5, 6, 7.5, 9, 10.5, 12, 13.5, 15, 16.5, 18, 19.5, 21, 22.5, 24
That's 15 ages, all 1.5 years apart and 24 is 8 times 3.
So it checks.
Edwin