A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%,some at 9%,and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?
A)$252,000 at 8% $456,000 at 9%
$63,000 at 10%
B)$252,000 at 9% $456,000 at 8%
$63,000 at 10%
C)$252,000 at 8% $63,000 at 9%
$63,000 at 9%
D)$252,000 at 8% $63,000 at 9%
$63,000 at 10%
E)$252,000 at 8% $63,000 at 9%
$456,000 at 10%

Question

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%,some at 9%,and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%? ​
A)$252,000 at 8% $456,000 at 9%
$63,000 at 10%
B)$252,000 at 9% $456,000 at 8%
$63,000 at 10%
C)$252,000 at 8% $63,000 at 9%
$63,000 at 9%
D)$252,000 at 8% $63,000 at 9%
$63,000 at 10%
E)$252,000 at 8% $63,000 at 9%
$456,000 at 10%

Quizplus · Accepted Answer

Let's denote the amount borrowed at 10% as $x$, at 8% as $4x$ (since it's four times the amount at 10%), and at 9% as $y$. The total borrowed is $771,000, so we have the equation:$$x + 4x + y = 771,000$$$$5x + y = 771,000$$ (1)The total interest is $67,500, so we also have:$$0.10x + 0.08(4x) + 0.09y = 67,500$$$$0.10x + 0.32x + 0.09y = 67,500$$$$0.42x + 0.09y = 67,500$$ (2)Given that the amount borrowed at 8% is four times the amount borrowed at 10%, we solve these equations simultaneously to find the values of $x$ and $y$, and subsequently, $4x$.Solving these equations gives us:$x = 63,000$ (at 10%),$4x = 252,000$ (at 8%),and the remainder for 9% is $771,000 - 63,000 - 252,000 = 456,000$.Therefore, the correct distribution is $252,000 at 8%, $456,000 at 9%, and $63,000 at 10%.

A Small Corporation Borrowed $771,000 to Expand Its Clothing Line