Financial mixture problems

Question

Sam has $120,000 invested in an account that pays 4.5% interest. How much would he need to invest in an account that pays 5.7% interest to raise his combined yield to 5%? 

 

How do I do this problem? What is the easiest way to obtain the answer and the question that they are asking? 

Answer 1

.045(120,000) + .057X = .05(120,000+ X)

.045(120) + .057X = .05(120+X) measured in thousands

5.4 + .057-.05X = 6.0

.007X =.6

X =.6/.007 = 6/.07 =about $85,714.29 invested at 5.7% will make the average return 5%

.045(120,000) = $5,400 interest

.057(85,714.29) = $4885.71

.05(205,714.29) =$10,285.71