Question 830326
A girl is the eldest of 15 children and each child is exactly a year and a half apart. 
<pre>
Their ages form an arithmetic sequence with n=15 terms and common
difference d=1.5.  So we use the formula:

a<sub>n</sub> = a<sub>1</sub> + (n-1)d

a<sub>15</sub> = a<sub>1</sub> + (15-1)(1.5)

a<sub>15</sub> = a<sub>1</sub> + (14)(1.5)

a<sub>15</sub> = a<sub>1</sub> + 21
</pre>
The eldest is eight times the youngest age
<pre>
The eldest's age is a<sub>15</sub>
The youngest's age is a<sub>1</sub>

So we have the system of two equations in two unknowns: 

{{{system(a[15] = a[1] + 21,a[15] = 8a[1])}}}  

Solve by substitution or elimination and get

a<sub>1</sub> = 3 and a<sub>15</sub> = 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</pre>