Answer
We invest 2166.66667 dollars, which is approximately 2167 dollars at 5%.
We invest 3833.33333 dollars, which is approximately 3833 dollars, at 7%,
Work Step by Step
Let X represent the amount invested at 5%.
The remainder, which is 6000 - X, will be invested at 7%.
From the first investment we will earn 5% $\times$ X = 0.05X.
From the second investment we will earn .07 $\times$ (6000 - X) =
420 - 0.07X.
We know that the interest earned by the 5% investment is 160 less than the interest earned by the 7% investment, so we set up the following equation:
0.05X + 160 = 420 - 0.07X
0.12X = 260
Divide both sides by 0.12:
X = 2166.66667 dollars, which is approximately 2167 dollars.
We invest 2166.66667 dollars, which is approximately 2167 dollars at 5%.
We invest 6000 - 2166.66667 = 3833.33333 dollars, which is approximately 3833 dollars, at 7%.
