Suppose you invested $10,000 part at 6% annual interest and the rest at 9% annual interest. If you received $684 in interest after one year, how much did you invest at each rate?
Assuming simple interest (i.e. no compounding within first year), then At 6%, interest = 10000*0.06=$600 At 9% interest = 10000*0.09 = $900
Two ways to find the ratio method A. let x=proportion at 6% then 600x+900(1-x)=684 Expand and solve 300x=900-684=216 x=216/300=0.72 or 72% So 10000*0.72=7200 were invested at 6% 10000-7200=2800 were invested at 9%
method B: by proportions Ratio of investments at 6% and 9% = 900-684 : 684-600 =216 : 84 = 18 : 7 Amount invested at 6% = 18/(18+7) * 10000 = 0.72*10000 = 7200 Amount invested at 8% = 7/(18+7)*10000=0.28*10000=2800
