really need help please

Question

A bank loaned out ​$11,000​, part of it at the rate of 9 % per year and the rest at 19 % per year. If the interest received in one year totaled ​$1500​, how much was loaned at 9 % ?

How much of the ​$11,000 did the bank loan out at 9 % ?

Answer 1

$5900 at 9%

You can use substitution with a system of equations to calculate the distribution of funds. We know we had a total of $11000 loaned out some at 9% and some at 19% for a total interest of $1500 after one year. Keep in mind that the interest rates above need to be expressed as decimals in the calculations below.

Equation 1 represents the total funds loaned out

x + y = 11000

and therefore

y = 11000 - x

Equation 2 represents the rates to obtain the total interest

.09x + 0.19y = 1500

If we substitute 11000 -x for y in Equation 2 we can solve for x.

0.09x + 0.19(11000 - x) = 1500

0.09x + 2090 - 0.19x = 1500

Combine like terms

-0.10x + 2090 = 1500

Subtract 2090 from both sides of the equation

-0.10x = 1500 - 2090

-0.10x = -590

Divide both sides by -0.10

x = 5900

We can use this in Equation 1 to solve for y

y = 11000 -x = 11000 - 5900 = 5100

y = 5100

Now we can check both values in Equation 2

.09(5900) + 0.19(5100) = 1500

531 + 969 = 1500

1500 = 1500

and from Equation 1

5900 + 5100 = 11000

The work can also be done by elimination as another check and you can give that a try.

I hope you find this useful and if you have any question please send me a message.