SOLUTION: Jake invested one-third of his money at 9.75% and the rest at 11.5%. At the end of 18 months he had earned $4,912.50 in simple interest. Find the total amount of money invested.

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Jake invested one-third of his money at 9.75% and the rest at 11.5%. At the end of 18 months he had earned $4,912.50 in simple interest. Find the total amount of money invested.      Log On

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Question 166706: Jake invested one-third of his money at 9.75% and the rest at 11.5%. At the end of 18 months he had earned $4,912.50 in simple interest. Find the total amount of money invested.
Answer by aswathytony(47) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the total amount of money invested.
given,one third invested in 9.75%
i.e. x/ 3 amount invested in 9.75 %
rest of money= x - x /3 = x ( 1 - 1/3 )
= x . 2/3
2/3 x
i.e. 2/3 x of total amount invested in 11.5%
given total amount = $4912.50
Total amount = principal + interest ( SI = pnr/100 ) n= 18month = 3/2yrs
4912.50 = x + [ (x/3 * 3/2 * 9.75 )/100 + (2/3x * 3/2 *11.5)100]
= x + 0.39 x /8 +2.3x /20 (canceling common terms in each
term)
4912.50 = 40 x + 1.95 x + 4.6x /40 ( taking LCM & Multiplying)
=46.55x /40
4912.50 * 40 =46.55x
196,500 = 46.55x
x = 196500/46.55
= 4221.27
Amount invested = $4221.27