I'm trying to solve the following problem but the result I'm getting is not logical given the data of the problem.
Pat invested a total of \$30,000. Part of the money was invested in a money marketing account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the interest earned at the end of the first year from these investments was \$256, how much did Pat invest at 10 percent and how much at 8 percent?
I got the following two formulas from the problem:
$$x + y = 3000$$
$$x\left (1 + \frac{10\left (1 \right )}{100} \right ) + y\left (1 + \frac{8\left (1 \right )}{100} \right ) = 256$$
To calculate the simple interest I'm using the following formula:
$$V=P\left ( 1 + \frac{rt}{100} \right )$$
where:
$V$ = Investment
$t$ = years
$P$ = amount of money invested
$r$ = simple annual interest rate
Using the elimination method, $y$ has a value of $152,200$, which is not logical.
Can someone tell me what I'm doing wrong?
Best regards,
The interest earned on $x$ is $10\%$ of $x$, not $110\%$ of $x$. Similar for the $y$ term.