Question

Theodore invests a total of $17,500 in two accounts paying 2% and 12% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $950.00.

Answer 1

Answer:

11,500 at 2% and $6,000 at 12%.

Step-by-step explanation:

Let x represent amount invested at 2% and y represent amount invested at 12%.

We have been given that Theodore invests a total of $17,500 in two accounts. We can represent this information in an equation as:

$x+y=17500...(1)$

$x=17500-y...(1)$

We are also told that he invested $17,500 in two accounts paying 2% and 12% annual interest, respectively. After one year, the total interest was $950.00.

Interest earned at 2% in one year would be $0.02x$.

Interest earned at 12% in one year would be $0.12y$

$0.02x+0.12y=950...(1)$

Upon substituting equation (1) in equation (2), we will get:    

$0.02(17500-y)+0.12y=950$

$350-0.02y+0.12y=950$

$350+0.10y=950$

$350-350+0.10y=950-350$

$0.10y=600$

$\frac{0.10y}{0.10}=\frac{600}{0.10}$

$y=6000$

Therefore, Theodore invested $6,000 at 12%.

Upon substituting $y=6000$ in equation (1), we will get:

$x=17500-6000$

$x=11500$

Therefore, Theodore invested $11,500 at 2%.