Question

William opened two investment accounts. The first​ year, these​ investments, which totaled ​$1800​, yielded ​$105 in simple interest. Part of the money was invested at 6.5​% and the rest at 5​%. How much was invested at each​ rate?

Answer 1

Answer:

$1000 at a 6.5% rate

$800 at a 5% rate

Explanation:

Let X be the amount invested at a 6.5% rate and Y be the amount invested at a 5% rate.

$X+Y = \ 1800\\0.065X+0.05Y=\ 105$

Solving the linear system:

$X+Y -20*(0.065X+0.05Y)= \ 1800-(20*\ 105)\\-0.3X=-\ 300\\X=\ 1000\\Y= \ 1800-\ 1000\\Y=\ 800$

$1000 were invested at a 6.5% rate and $800 at a 5% rate.