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?
If x is invested at 8% then the rest (5200-x) is at 10%
so, add up the interest
.08x + .10(5200-x) = 496
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that Carmen invested x dollars at 8% and (5200 - x) dollars at 10%.
The interest earned from the money invested at 8% can be calculated using the formula: Interest = Principal x Rate x Time. In this case, the rate is 8% (or 0.08) and the time is one year. So, the interest earned from the money invested at 8% is 0.08x.
Similarly, the interest earned from the money invested at 10% is 0.10(5200 - x).
According to the given information, Carmen earned a total of $496 in interest. Therefore, we can write the following equation:
0.08x + 0.10(5200 - x) = 496
Now, let's solve this equation to find the value of x:
0.08x + 0.10(5200 - x) = 496
0.08x + 520 - 0.10x = 496
0.08x - 0.10x = 496 - 520
-0.02x = -24
Dividing both sides of the equation by -0.02:
x = -24 / -0.02
x = 1200
Therefore, Carmen invested $1200 at 8% and $4000 (5200 - 1200) at 10%.