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<p>While the situation described by the OP (for someone else, not the OP) may be a common situation, the price and financial aid policies of in-state public universities vary by state. In California, the UCs tend to be very competitive on net price for the situation described by the OP. For a Pennsylvania resident in this situation, the state(-related) schools tend to be rather uncompetitive on net price, due to their poor in-state financial aid. So using other states makes no sense for this comparison.</p>
<p>Of course, the student and family described by the OP may choose to pay a premium over UCR or other UC to attend a LAC (since they have a $20,000 budget, but the apparent safety UCR is apparently only about $14,000, they have about $6,000 of budget leeway here). But that is not the same as saying that the LACs in question will cost less than a state university for them. (Also, if the student does choose to major in math, he needs to check LACs carefully for their offerings in that subject.)</p>