Do you know what the exact model # on the side of the RAM is? That would be helpful.
As for the CPU and motherboard:
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($85.50 @ SuperBiiz)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($71.10 @ SuperBiiz)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($44.10 @ SuperBiiz)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($38.70 @ SuperBiiz)
Total: $239.40
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-05-20 00:31 EDT-0400
Dragon Age can use 6 cores so it would make complete sense to go with a 6300 rather than not. And Sims 4 can be played on a calculator so there is no worries there.
But there is also the Intel path which would be less expensive and (should) give identical performance in those games. Not too sure about Dragon Age though. But that game isn't very demanding so it should be completely fine. It would also be the best solution if she is planning on using the computer for every day tasks like word docs, we surfing, etc..
Without further adieu:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i3-4150 3.5GHz Dual-Core Processor ($93.99 @ SuperBiiz)
Motherboard: Gigabyte GA-H81M-DS2V Micro ATX LGA1150 Motherboard ($48.99 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($44.10 @ SuperBiiz)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($38.70 @ SuperBiiz)
Total: $225.78
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-05-20 00:48 EDT-0400
Don't be fooled by the dual-coreness of the i3. It has few, very strong cores unlike the 6300's many, weaker cores.