Thomas invested $8,500 for one year. Part of the money was invested at6% and the rest at 9%. The total interest earned was $667.50. How much did Thomas invest at the 6% rate?

Okay so say that x=amount invested with 6% and y=amount invested with 9%

x+y=8,500 so > x=8500-y

6%=0.06 9%=0.09

0.06x + 0.09y=667.5 (Substitute in x=8500-y so only numbers and y)

0.06 (8500-y) + 0.09y=667.5 (expand brackets)

510-0.06y+0.09y=667.5 (-510)

0.03y=117.5 (/0.03)

$3916.67=Y - >9%

X=8500-Y

x=$4583.33 - >6%