SOLUTION: Kate has a t-shirt business that has earned a total of $15 000 this year. She invests part of the money at 4% per year and the rest at 5% per year. After one year she earned $690

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Question 1169392: Kate has a t-shirt business that has earned a total of $15 000 this year. She invests part of the
money at 4% per year and the rest at 5% per year. After one year she earned $690 in interest.
How much did she invest at each rate?
Found 3 solutions by The Troll Kid, Solver92311, greenestamps:
Answer by The Troll Kid(22) About Me  (Show Source):
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


If a portion of monetary units are invested at per calendar period and the balance at per calendar period and the entire investment earns monetary units in interest for one calendar period, then if represents the portion of the investment earning interest, the amount invested at each rate can be calculated by solving:



for and then calculating

John

My calculator said it, I believe it, that settles it

From
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A quick and easy non-algebraic method for solving this kind of problem....

(1) All $15,000 invested at 4% would yield $600 interest; all at 5% would yield $750 interest.
(2) The actual interest, $690, is 90/150 = 3/5 of the way from $600 to $750. (Picture the 3 numbers on a number line if it helps....)
(3) Therefore, 3/5 of the total was invested at the higher rate.

ANSWER: 3/5 of the $15,000, or $9000, at 5%; the other $6000 at 4%.

CHECK: .05(9000)+.04(6000) = 450+240=690