SOLUTION: Miss Santos invested half of her money at 1% and half at 8% per year. Her annual income from the two investments was 7,500 pesos. How much did she invest at each rate?

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Question 92923: Miss Santos invested half of her money at 1% and half at 8% per year. Her annual income from the two investments was 7,500 pesos. How much did she invest at each rate?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let us suppose that Miss Santos had money amounting to 2x pesos.
So she invested x pesos at 1% and x pesos at 8% simple interest per annum.

Interest on x pesos for 1 yr at 1% simple interest per annum = x%2A1%2F100+=+x%2F100 pesos.
Amount at 1% rate = Principal + Interest = x+%2B+x%2F100+=+109x%2F100 pesos.
Interest on x pesos for 1 yr at 8% simple interest per annum = x%2A8%2F100+=+2x%2F25 pesos.
Amount at 8% rate = Principal + Interest = x+%2B+2x%2F25+=+27x%2F25 pesos.
Total annual income from the interests = 109x%2F100+%2B+27x%2F25+=+217x%2F100 pesos.

This amount is equal to 7500 pesos.
So 217x%2F100+=+7500
or x+=+750000%2F217+=+3456.22

So Ms. Santos invested 3456.22 pesos at each rate.