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Prince Neva Ben Rich takes out two loans. He borrows $800 more from a credit union that charges 12% interest than from a bank that charges 15% interest. If his interest payments total $420 annually, how much does he borrow at each rate?

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Sophos
$2000 from Credit Union
$1200 from Bank
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Answer:

Step-by-step explanation:

Given that Prince Neva Ben Rich takes out two loans. He borrows $800 more from a credit union that charges 12% interest (say x) than from a bank that charges 15% interest (say y)

Given that total interest = 420

i.e. [tex]0.12x+0.15y =420\\x =y+800[/tex]

We have two independent equations in two variables.

Substitute x value in the I equation to get

[tex]0.12(y+800)+0.15y = 420\\0.27y =420-96 =324\\y = \frac{324}{0.27} =1200\\x = 1200+800 =2000[/tex]

He borrowed 2000 from credit union and 1200 from other bank.

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