SOLUTION: Robert inherited $4000 from his grandmother. Part was invested at 5% while the rest was invested at 6 1/2%. The interest for a year was $227. How much was invested at 6 1/2 perc

Question 5160: Robert inherited $4000 from his grandmother. Part was invested at 5% while the rest was invested at 6 1/2%. The interest for a year was $227. How much was invested at 6 1/2 percent.
My book says the answer is $1,800. I have tried and tried, yet my answer is far from their answer. Please help me.
Answer by guapa(62) (Show Source): You can put this solution on YOUR website!
Let x represent the amount invested at 6 1/2%. Then 4000-x represents the amount invested at 5%.
So, as a guideline you can use the following:
Interest earned from 6 1/2% + Interest earned from 5% = Total interest earned
6 1/2%(x)+ 5%(4000-x) = 227
First express the % in decimals: 6 1/2% = 0.065, 5%= 0.05
Now we can set up the following equation:
0.065(x) + 0.05(4000-x)= 227
0.065x + 200 - 0.05x = 227
0.015x = 227
x = 1800
The amount investest at 6 1/2% is $1800.
You can check it by using the simple interest formula:
i=Prt
i= 1800*0.065 = 117
i= 2200*0.05 = 110
117+110 = 227
Hope it helps
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