Question 41616: Lane invested $10,000, part at 15% and part at 14%.
If the total interest at the end of the year is $1,430, how much did she invest at 15%?
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! This is a type of mixture problem.
The formula to remember is:
(rate of A)(amount of A) + (rate of B)(amount of B) = Total Value
Rate A = 15% = .15
Amount A = "how much" = x
Rate B = 14% = .14
Total Value = "the total amount of interest" = $1430 (this wording is confusing because this is really the "Total Value of interest of $10,000)
.
Total Amount invested = $10,000 =(Amount of A + Amount B)
So, 10,000 - A = B
or 10,000 - B = A
.
Putting it all together:
(.15)(x) + (.14)(10,000 - x) = 1430
Simplifying:
.15x + (1400 -.14x) = 1430
.15x + 1400 - .14x = 1430
.01x + 1400 - 1400 = 1430 - 1400
.01x = .30
.01x/.01 = 30/.01
x = 3000
.
Plugging x=3000 back into the original equation:
(.15)(x) + (.14)(10,000 - x) = 1430
(.15)(3000) + (.14)(10,000 - 3000) = 1430
450 + 980 = 1430
1430 = 1430
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