35) juan deposits $750 into an account. he was told that his balance will double every 8.5 years. virginia deposits $500 into a separate account. her money will triple, every 10 years. after a certain number of years they will both have the same amount in their accounts. how many years will it take for this to happen?

We will have to solve for the rate of both accounts.
We'll use this complicated formula:
log(1 + rate) = {log(total) -log(Principal)} ÷ Years

One account doubles the money every 8.5 years:
(We'll make total = 2 and principal = 1)
log(1 + rate) = {log(2) -log(1)} ÷ 8.5
log(1 + rate) = 0.30102999566 / 8.5
log(1 + rate) = 0.0354152936
10^0.0354152936 = 1.0849639136
rate = 8.49639136

The other account triples the money every 10 years:
(We'll make total = 3 and principal = 1)
log(1 + rate) = {log(3) -log(1)} ÷ 10
log(1 + rate) = 0.47712125472 / 10
log(1 + rate) = 0.047712125472
10^0.047712125472 = 1.116123174
rate = 11.6123174

Okay, NOW we have to calculate when will $750 invested at 8.49639136 interest equal $500 invested at  interest 11.6123174?

That seems difficult to solve exactly because we have 2 unknowns:
We don't know the AMOUNT of money when one account equals the other and we don't know the TIME it will take.

Amount 1 = 750 * (1.0849639136)^years
Amount 2 = 500 * (1.116123174)^years

I don't know how to solve for those equations when Amount 1 = Amount 2. 
However, I was able (by trial and error) to determine a precise answer. 
In 14.32005 years, both accounts will equal $2,411.07.