A bank loaned out $17,000 , part of it at the rate of 9 % per year and the rest at 17 % per year. If the interest received in one year totaled $2,000 , how much was loaned at 9 %? How much of the $17,000 did the bank loan out at 6%?

1) bank loaned at 9% = $11,066

2) bank loaned at 17% = $5,934

3) bank loaned at 6% = $1,020

Step-by-step explanation:

Step 1:

assume;

1) x is the amount loaned for 9%

2) y is the amount loaned for 17%

3) z is the internet amount received after one year = $2,000

4) A is total amount loaned = $17,000

Step 2:

bank loaned $17,000 for 9% and 17% interest therefor;

A=X+Y

17000 = X + Y

For X;

X=17000-Y

Step 3:

Interest received at the end of one year will be;

Z = (X*9%) + (Y*17%)

2000 = X (9/100) + Y (17/100)

2000 = X (0.09) + Y (0.17)

For X;

X (0.09) = 2000-0.17Y

X = (2000-0.17Y) / 0.09

X = (2000/0.09) - (0.17/0.09) Y

X = 22,222 - 1.88Y

Step 4:

We have two values of X from Step 2 and 3, now compare both;

17000-Y = 22,222 - 1.88Y

For Y

1.88Y - Y = 22,222-17,000

0.88Y = 5,222

Y = 5,222/0.88

Y = $5,934

Step 5:

For X;

X=17,000-Y

X = 17,000-5,934

X = $11,066

Step 6:

For last question that is how much bank loaned for 6%, assume it is B;

B = 17,000 * 6%

B = 17,000 * (6/100)

B = 17,000 * 0.06

B = $1,020