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A small corporation borrowed $1,000,000 to expand its line of toys. Some of the money was borrowed at 7%, some at 8%, and some at 9%. How much was borrowed at each rate if the annual interest owed was $74,000 and the amount borrowed at 7% was five times the amount borrowed at 9%

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Answer:

$750,000 at 7%

$150,000 at 9%

$100,000 at 8%

Explanation:

Let 'S' be the amount borrowed at 7%, 'E' be the amount at 8% and 'N' be the amount borrowed at 9%. The following system of equations can be modeled with the given data.

[tex]S+E+N=1,000,000\\0.07S+0.08E+0.09N=74,000\\S=5N\\[/tex]

Solving the system:

[tex]E+6N=1,000,000\\0.08E+0.44N=74,000\\\\-0.0909090E=-9,090.9091\\E=100,000\\N=\frac{1,000,000-100,000}{6}=\$150,000\\S=5*\$150,000=\$750,000[/tex]

Therefore, the corporation borrowed $750,000 at 7%, $150,000 at 9% and $100,000 at 8%.

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