A bank loaned out $13 comma 00013,000, part of it at the rate of 6 %6% per year and the rest at 16 %16% per year. If the interest received in one year totaled $15001500, how much was loaned at 6 % question mark

Given

Bank loaned = $13,000

Part of it at 6%

and the rest at 16%

If interest received in one year = $1500, how much was loaned at 6%?

Setting Variables:  

x = Total Dollar Amount loaned at 6%  

y = Total Dollar Amount loaned at 16%

so,  

x + y = $13,000   > eq.(1)

Now the overall Equation for the Interest is  

$1,500 = 0.06*x + 0.16*y

Substitute for y, in terms of x using eq.(1), which is y= 13,000-x

1,500 = (0.06*x + 0.16* (13,000-x))

1,500 = 0.06x + 2,080 - 0.16x

1,500-2,080 = -0.10x

-580 = -0.10x

Finally x = 5,800, which is loaned at 6%

a is the right answer