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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?

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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.

[tex]X+Y = \$1800\\0.065X+0.05Y=\$105[/tex]

Solving the linear system:

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

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

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