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A bank loaned out $17,000, part of it at the rate of 8% per year and the rest at 16% per year. If the interest received in one year totaled $2000, how much was loaned at 8%?How much of the $17,000 did the bank loan out at 8%?how much of the $17,000 did the bank loan out of the 8%

Respuesta :

The given information is:

- The bank loaned out $17,000.

- One part at a rate of 8% and the rest at 16%, per year.

- The total interest received in one year totaled $2000.

Let's set x the part loaned at 8% and y the part loaned at 16%. So:

[tex]\begin{gathered} x+y=17000\text{ Equation 1} \\ x*0.08+y*0.16=2000\text{ Equation 2} \end{gathered}[/tex]

First, find x in terms of y from equation 1:

[tex]x=17000-y[/tex]

Now, replace x in equation 2 and solve for y:

[tex]\begin{gathered} (17000-y)0.08+0.16y=2000 \\ 1360-0.08y+0.16y=2000 \\ -0.08y+0.16y=2000-1360 \\ 0.08y=640 \\ y=\frac{640}{0.08} \\ \\ y=8000 \end{gathered}[/tex]

Replace y in and solve for x:

[tex]\begin{gathered} x=17000-8000 \\ x=9000 \end{gathered}[/tex]

So, the bank loaned $9000 at 8% and $8000 at 16%.

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