let the final interest = X
If Simple interest is given A=PiN, where A is the final interest, P is the principal, i is the rate of interest and N is the number of terms (years)
∴The first account will be X = H x 0.06 x 1, where H is the principal for that account
And the second account will be X = G x 0.09 x 1, where G is the principal for that account
You can substitute the X value of the first equation (X = P x 0.06 x 1) into the second equation to make:
H x 0.06 = G x 0.09
∴G = 2/3 x H
∴G/H = 2/3 (makes a ratio of five parts)
Divide 7200 into five parts = $1440 per part
Hence, G = 2 x 1440 = $2880, and H = 3 x 1440 = $4320
