Question 1080100: Using I= PRT. Madison invested a total of $30,000 at two different banks. At one bank she earned 3.5% on her investment and at the other bank she earned 4.5%. If her total earnings are $1,320 then how much did she invest at each bank?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula is i = prt.
i is the interest
r is the interest rate per time period.
t is the number of time periods.
the assumption here is that t = 1 year, even though they didn't tell you that.
therefore, if t = 1, then the formula becomes i = pr.
if you let x = the principal from the first bank and y equal the principal from the second bank, then the formula for each bank becomes:
i = xr for the first bank
i = yr for the second bank.
if you let r = .035 for the first bank and you let r = .045 for the second bank, then the formula becomes:
i = .035x for the first bank and i = .045y for the second bank.
note that interest rate is equal to interest rate percent / 100.
consequently 3.5% equals .035 and 4.5% equals .045
your total principal is equal to 30,000
consequently x + y = 30,000
your total interest is equal to 1320.
consequently .035x +.045y = 1320
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 30,000
.035x + .045y = 1320
you solve this like you solve any other set of simultaneous equations.
i'll do this one by substitution.
in the first equation, solve for y to get y = 30,000 - x
in the second equation, replace y with 30,000 p x to get:
.035x + .045(30,000 - x) = 1320
simplify to get .035x + 1350 - .045x = 1320 *****
***** looks like you have a problem because the interest on the second bank is higher then the interest on both banks.
we'll work it through and see what happens.
starting again from simplify:
simplify to get .035x + 1350 - .045x = 1320
combine like terms to get .08x + 1350 = 1320
subtract 1350 from both sides of the equation to get:
.08x = 1320 - 1350 which results in:
.08x = -30
solve for x to get x = -30/.08 = -375.
there's the problem caused by the interest in the second bank being higher than the overall interest.
either the problem is wrong or you copied it wrong.
go back and check to make sure you got the figures right.
the combined interest has to be higher than the sum of the interest earned at each bank.
the interest earned at each bank has to be lower than the combined interest.
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