Question 763000
If she is n years old, the money she would have got so far = 

1+2+3+4....+n = 2145

The left side is an arithmetic progression with 1st term as 1, difference as 1 and n terms. (It is in fact the sum of the 1st n integers starting from 1)

It is given by n*(n+1)/2 = 2145

{{{n*(n+1)/2 = 2145}}}

Simplifying, {{{n^2 + n - 4290 = 0}}}

Factorizing:

{{{(n+66)*(n-65) = 0}}}

n = -66, or n = 65.

Since age cannot be negative, Joanie is {{{highlight(65)}}} years old.

The above quadratic equation also be solved using the standard formula as shown below, which gives  the solutions as n = -66 or n = 65.

:)

*[invoke quadratic "x", 1, 1, -4290 ]