SOLUTION: Katie invested a total of $7000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $250 interest. How mu

Question 1146610: Katie invested a total of $7000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $250 interest. How much was invested at each rate?
Found 2 solutions by richwmiller, greenestamps:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x+y=7000
.03x+.04y=250
Answer by greenestamps(13196) (Show Source): You can put this solution on YOUR website!

A non-traditional, non-algebraic solution method....

The fraction of the total invested at the higher rate is exactly determined by where the actual interest lies between the amounts of interest that would have been earned at the two rates.

(1) all $7000 at 3% --> $210 interest
(2) $7000 split --> $250 interest (given)
(3) all $7000 at 4% --> $280 interest

From 210 to 280 is 70; from 210 to 250 is 40. 40/70 = 4/7.

The actual interest of $250 is 4/7 of the way from $210 to $280, so 4/7 of the total was invested at the higher rate.

ANSWER: 4/7 of the $7000, or $4000, at 4%; the other $3000 at 3%.

CHECK: .04(4000)+.03(3000) = 160+90 = 250
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SOLUTION: Katie invested a total of ​$7000​, part at 3​% simple interest and part at 4​% simple interest. At the end of 1​ year, the investments had earned ​$250 interest. How mu

SOLUTION: Katie invested a total of $7000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $250 interest. How mu