Abank 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

2nd one in the first row is correct

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.