# A man invests some money at 5%, and $49,000 more than three times the amount at 11%. The total annual interest earned from the investment is$51,370. How much did he invest at each amount?

Dec 20, 2017

$121,000 was invested at 5% $412,000 was invested at 11%

#### Explanation:

There is a given relationship between the two amounts, so you can define them using one variable.

Let the amount at 5% be $x$.
Therefore the larger amount at 11% is $3 x + 49 , 000$

Now form an equation - you know the total amount of interest is $51 , 370$

'Interest at 5% + Interest at 11% = 51,370

$\frac{5}{100} \times x + \frac{11}{100} \times \left(3 x + 49000\right) = 51370 \text{ } \leftarrow \times 100$

$5 x + 11 \left(3 x + 49 , 000\right) = 51 , 370$

$5 x + 33 x + 539 , 000 = 5 , 137 , 000$

$38 x = 5 , 137 , 000 - 539 , 000$

$38 x = 4 , 598 , 000$

$x = 121 , 000$

$121 \times 3 + 49000 = 412 , 000$