Algebra Homework help

Question

Solve the problem.

A loan officer at a bank has $100,000 to lend and is required to obtain an average return of  per year. If he can lend at the rate of  or the rate of  how much can he lend at the  rate and still meet his required return?

Answer 1

14-13 = 1

13=11 =3

3/1 = 2

2 times as much 14% is needed as 11% to get 13%. 2/3 of $100,000 is invested at 14%

It's a ratio of 2:1. 100,000 divided into 2/3 gives $66,666.67 invested at 14% and $33,333.33 invested at 11%

.14(66 2/3) + .11(33 1/3 = .13(100)

9 1/3 + 3 2/3 = 13

.14x + .11(100-x) = .13(100)

.14x -.11x = .13(100)-.11(100)

.03x = .02(100) = 2

x = 2/.03 = 200/3 = 66 2/3 thousand dollars = $66,666.67 invested at 14%

100-x = 33 1/3 = $33,333.33 invested at 11%