Yes she will have have money to buy all the toppings
6,612 is the answer because all you need to do is combine them by their place value.
The sum of n terms of a geometric series is found using the following formula:
![S _{n} = \frac{a(1-r^{n})}{1-r}](https://tex.z-dn.net/?f=S%20_%7Bn%7D%20%3D%20%5Cfrac%7Ba%281-r%5E%7Bn%7D%29%7D%7B1-r%7D%20)
where a is the first term and r is the common ratio.
In your question, a = 6 and r = 1/3, so we have:
![S_{5} =\frac{6(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}](https://tex.z-dn.net/?f=%20S_%7B5%7D%20%3D%5Cfrac%7B6%281-%28%5Cfrac%7B1%7D%7B3%7D%29%5E5%29%7D%7B1-%5Cfrac%7B1%7D%7B3%7D%7D)
which simplifies to:
1- $52 {40+12(1)=}
5- $100 {40+12(5)=}
10 - $160 {40+12(10)=}
50 - $640 {40+12(50)=}