how can $57,000 be invested, part at 8% annual simple interest and the remainder at 11% annual simple…

how can $57,000 be invested, part at 8% annual simple interest and the remainder at 11% annual simple interest, so that the interest earned by the two accounts will be equal? the amount to invest at 8% is $

how can $57,000 be invested, part at 8% annual simple interest and the remainder at 11% annual simple interest, so that the interest earned by the two accounts will be equal? the amount to invest at 8% is $

Answer

Explanation:

Step1: Let the amount invested at 8% be $x$.

Then the amount invested at 11% is $(57000 - x)$.

Step2: Set up the interest - equality equation.

The simple - interest formula is $I=Prt$. Since $t = 1$ year, the interest from the 8% investment is $0.08x$, and the interest from the 11% investment is $0.11(57000 - x)$. Set them equal: $0.08x=0.11(57000 - x)$.

Step3: Expand the right - hand side of the equation.

$0.08x = 0.11\times57000-0.11x$. $0.08x=6270 - 0.11x$.

Step4: Add $0.11x$ to both sides of the equation.

$0.08x + 0.11x=6270$. $0.19x = 6270$.

Step5: Solve for $x$.

$x=\frac{6270}{0.19}=33000$.

Answer:

$33000$