SOLUTION: Joanie got money from her uncle on every birthday. The amount of money he gives her is equal to her new age. (When she turned 5 he gave her $5, when she turned 7 he gave her $7, et

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Question 763000: Joanie got money from her uncle on every birthday. The amount of money he gives her is equal to her new age. (When she turned 5 he gave her $5, when she turned 7 he gave her $7, etc) She always put the money in a special box, rather than spend it. She now has $2145 in the box. How old is she?
Answer by ramkikk66(644)   (Show Source): You can put this solution on YOUR website!
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

Simplifying,
Factorizing:

n = -66, or n = 65.
Since age cannot be negative, Joanie is 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.
:)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=17161 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 65, -66. Here's your graph:
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