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Carmen invests a total of $5200. Some of the money is invested at 8%. The rest is invested at 10%. If Carmen earned $496 of interest in one year, how much did she invest at each rate?

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If x is invested at 8% then the rest (5200-x) is at 10%
so, add up the interest
.08x + .10(5200-x) = 496

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