Hugh invested 33000, part @20% and part @3%. total interest at end of year 4390. how much did he invest @ 20%?

Answer 1

Let x be the amount invested at 20%.
Then the amount invested at 3% is 33000 - x.
The interest is:
0.2x + 0.03(33000 - x) = 4390
(0.2 - 0.03)x = 4390 - 990
0.17x = 3400
x = 340000 / 17 = 20000.

Hence 20000 was invested at 20% and 13000 at 3%.

Answer 2

This is a linear equation problem.

x + y = 33000

x(.20) + y(.03) = 4390

You need to solve for x.

x = 33000-y

(33000-y)(.20) + y(0.03) = 4390

6600 - 0.17y = 4390

2210 = 0.17 y

y = 13,000 (Invested at 3%)
x = 20,000 (Invested at 20%)

Answer 3

Hi,
You need to develop two equations: One that expresses the amount of money invested and one that expresses the interest earned. So, let’s translate your problem into algebra.
Amt @20% + Amt @ 3% = 33,000 (Eq #1) (Describes the money invested.)
.20*Amt @ 20% + .03*Amt @3% = 4390 (Eq #2) (Describes the interest.)

Now, let’s let:
X represent Amt @ 20%
And
Y = Amt @ 3%
Then we can rewrite our equations in terms of these unknowns as follows:
x + y = 33,000 (Eq 1b)
.20x + .03y = 4390 (Eq 2b)

If you have a graphing calculator such as a TI-83 Plus or a TI-84, you can solve this with matrices. I will cover that at the end of this discussion, but, for now, let’s continue doing it by hand.

20x + 3y = 439000 (Eq 2c) (Multiply Eq 2b by 100 to get rid of the decimals.)

Now, let’s solve these equations by solving Eq 1b for “y” and substituting that into Eq 2c.
x+y = 33,000
y = 33,000-x
Now, substitute into Eq 2c in place of y.
20x + 3(33000-x) = 439000
20x + 99000 -3x = 439000 (Distributive property.)
17 x = 340,000 (Combine like terms and subtract 99000 form both sides of the equation.)
x = 20,000
Now, find y from Eq 1
X + y = 33,000
20,000 + y = 33,000
y = 17,000
==================
Solving with matrices and graphing calculator.
1) Entering a matrix:
a) Press 2nd, MATRIX, move the cursor to EDIT.
b) Move the cursor to the matrix number you want to edit or enter numbers into and press ENTER.
c) Enter the number of rows and press ENTER; then enter the number of columns and press ENTER.
d) Enter each value of the matrix and press ENTER after each value.
e) Press 2nd, QUIT to go to the home screen and solve for the reduced-row echelon form (rref).

2) Doing rref:
a) First enter your matrix as in item 1 of this section and press 2nd, QUIT to go to the home screen.
b) Press 2nd, MATRIX, and move the cursor to MATH.
c) Select item B for rref and press ENTER.
d) Press 2nd, MATRIX and press the number for the matrix you want to operate on. You should have rref([A] on the screen if your equations are in matrix [A].
e) Press ENTER and the answer will appear.

Hope this helps
FE

Answer 4

Let x = amount invested @ 20%, 33,000 - x = amount invested @ 3%.

Equation (finding value of x):
0.2x + 0.03(33,000 - x) = 4,390
0.2x + 990 + 0.03x = 4,390
0.17x = 3,400
x = 20,000

Answer: 20,000 was invested @ 20%

Proof (equality of both sides of the equation):
0.2(20,000) + 0.03(33,000 - 20,000) = 4,390
4,000 + 0.03(13,000) = 4,390
4,000 + 390 = 4,390

Answer 5

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