Question

A bank loaned out $30,000, part of it at the rate of 15% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $3,550.00. How much was loaned at each rate?

Answer 1

Answer:

x represent the value loaned at 15% and y represent the value loaned at 10%.

$x=11000$ and $y=19000$

Step-by-step explanation:

We are going to write a system of two linear equations. The first equation  will represent the total amount loaned.

$x+y=30000$

Now the second equation are will represent the interest earned for both loans.

$(x*0.15)+(y*0.10)=3550$

Then x represent the value loaned at 15% and y represent the value loaned at 10%. Now solving the equation system we have:

$x=30000-y$ using this in the other equation to find y

$((30000-y)0.15)+(0.10*y)=3550$

$4500-0.15y+0.10y=3550$

$4500-0.05y=3550$

$4500-3550=0.05y$

$950=0.05y$

$\frac{950}{0.05}=y$

$19000=y$

With the value of y we can find x

$x=30000-19000$

$x=11000$