There isn't much that can be purchased for $400. that will run Sims 3 and all expansions, without having a lot of problems due to having a processor or graphics that isn't powerful enough to run the game.
My best advice is to keep saving up your money. Specially if you want a good laptop that will play sims 3 even on low/med settings.
Here's an a couple of example laptops:
MSI GP60 LEOPARD-010;9S7-16GH11-010 15.6-Inch Laptop = Price: $699.99
http://www.amazon.com/MSI-GP60-LEOPARD-010-9S7-16GH11-010-15-6-Inch/dp/B00IQ4E0ZIIntel Core i5-4200M 2.5 GHz
8GB Memory
NVIDIA Geforce GT840M
Will run game on low/med settings.
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Dell Inspiron i7559-763BLK 15.6" = Price: $799.99
Full-HD Gaming Laptop (Core i5, 8GB RAM, 256GB SSD, NVIDIA GeForce GTX960M) with Windows 10
http://www.amazon.com/Dell-Inspiron-i7559-763BLK-Full-HD-GeForce/dp/B015PYYDMQIntel i5-6300HQ 2.3 GHz - Turbo up to 3.2 GHz
8 GB Memory
NVIDIA GeForce GTX 960M 4GB GDDR5
Will run game on Med/High Settings
** This laptop will run Sims 3, but will end up having to run it constantly on turbo which isn't the best. Play for short periods of time up to 2-hours to prevent overheating of the laptop. As it will get hot. And definitely recommend a cooling mat to help keep it cooler.
However, if you want a desktop. We might be able to find something in the $500 - $600 range. Though most of the desktops in this price range will need a new graphics card if you want med or high settings.
CybertronPC Patriot GM1293D Desktop (Black/Red) Price: $449.99
http://www.amazon.com/CybertronPC-Patriot-GM1293D-Desktop-Black/dp/B00D1KX2M4AMD A4-5300 ~ 3.40GHz
8GB Memory
Radeon HD 7480D
- Low/Medium settings
The video card can be upgraded at a later date.
Suggested video card:
GeForce GTX 750Ti = Price: $124.41
http://www.amazon.com/EVGA-GeForce-750Ti-GDDR5-Graphics/dp/B00IDG3IDOHope this helps,
MrsFlynn