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g A bank loaned out $17,000, part of it at the rate of 7% per year and the rest at 15% per year. If the interest received in one year totaled $2,000, how much was loaned at 7%

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hyderali230

Answer:

Amount of Loan @ 7% was $6,875

Explanation:

Let

Amount of Loan @ 7% = X

Amount of Loan @ 15% = Y

According to given condition

X + Y = 17000 ( Eq 01 )

X7% + Y15% = 2000

0.07X + 0.15Y = 2000 ( Eq 02 )

By multiplying ( Eq 01 ) with 3

3X + 3Y = 51,000 ( Eq 03 )

By multiplying ( Eq 02 ) with 20

1.4X + 3Y = 40000 ( Eq 04 )

By subtracting ( Eq 04 ) from ( Eq 03 )

3X + 3Y - (1.4X + 3Y) = 51,000 - 40,000

3X + 3Y - 1.4X - 3Y = 11,000

1.6X= 11,000

X = 11,000 / 1.6

X = 6,875

Placing Value of X in ( Eq 01 )

6,875 + Y = 17000

Y = 17000 - 6,875

Y = 10,125

Check:

0.07(6,875) + 0.15(10,125) = 2000

481.25 + 1,518.75 = 2,000

2,000 = 2,000

So

Amount of Loan @ 7% = X = $6,875

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