SOLUTION: An executive invests $21,000, some at 8% and the rest at 6% Annual interest. if he receive an annual return of &1,620, how much is invested at each rate At 8% interest = At 6% i

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Question 1163731: An executive invests $21,000, some at 8% and the rest at 6% Annual interest. if he receive an annual return of &1,620, how much is invested at each rate
At 8% interest =
At 6% interest =
Found 3 solutions by MathLover1, MathTherapy, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


let x be amount at 8% and y at 6%
x%2By=21000...solve for x
x=21000-y.........eq.1
8% =0.08 interest of x and 6%=0.06 interest of y gives us an annual return of &1620 :
0.08x%2B0.06y=1620....eq.2
----------------------------------substitute x from eq.1 in eq.2

0.08%2821000-y%29%2B0.06y=1620....eq.2..solve for y
1680+-+0.08y%2B0.06y=1620
1680+-+0.02y=1620
0.02y=1680+-1620
y=60%2F0.02
y=3000
go to
x=21000-y.........eq.1...substitute y
x=21000-3000
x=18000
so,
at 8% interest =&18000
at 6% interest =&3000


check:
0.08x%2B0.06y=1620....eq.2

0.08%2A18000%2B0.06%2A3000=1620
1440%2B180=1620
1620=1620->true



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

An executive invests $21,000, some at 8% and the rest at 6% Annual interest. if he receive an annual return of &1,620, how much is invested at each rate
At 8% interest =
At 6% interest =
Let amount invested at 8% be E

Then amount invested at 6% = 21,000 - E

We then get: .08E + .06(21,000 - E) = 1,620

.08E + 1,260 - .06E = 1,620

.08E - .06E = 1,620 - 1,260

.02E = 360

Amount invested in the 8%-fund, or 

You should now be able to find the amount invested in the 6% fund.

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


If a formal algebraic solution is not required, here is a quick and easy solution method.

(1) All $21,000 at 6% would yield $1260 interest; all at 8% would yield $1680 interest.
(2) The actual interest, $1620, is 6/7 of the way from $1260 to $1680. (Picture the three numbers on a number line -- 1260, 1620, and 1680. 1260 to 1680 is 420; 1260 to 1620 is 360; 360/420 = 6/7.)
(3) That means 6/7 of the total was invested at the higher rate.

ANSWER: 6/7 of the $21,000, or $18,000, was invested at 8%; the other $3000 was invested at 6%.

CHECK: .06(3000)+.08(18000) = 180+1440 = 1620