I am having issues solving this word problem

Question

A university invests $600,000 at simple interest, part at 6%, half that amount at 4.5%, and the rest at 3.5%. What is the most that the university can invest at 3.5% and be guaranteed at least $24,600 in interest per year

Answer 1

Interest = Principle*Rate*Time

 

In this problem you have three rates and the principle is split between them.  Let 2x be the amount invested at 6%.  The amount invested at 4.5% is half of that, or x.  The amount invested at 3.5% is thus $600,000 - 3x.

 

$24,600 = 2x*(0.06)*(1 year) + x*(0.045)*(1 year) + ($600,000-3x)*(0.035)*(1 year)

 

$24,600 = 0.12x + 0.045x + 21,000 - 0.105x

 

$24,600 = .06x + 21,000

 

Solve for x.  Remember that the amount invested at 3.5% is $600,000-3x.