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3 years ago

You invested $21,000 in two accounts paying 2% and 4% annual interest, respectively.

Mathematics

2 answers:

Murrr4er [49]3 years ago

7 0

Answer:

$12,000 at 4%
$9,000 at 2%

Step-by-step explanation:

If x represents the amount invested at 4%, then the total interest earned is ...

0.04x + 0.02(21000 -x) = 660

0.02x = 240 . . . . . . . . . . . simplify, subtract 420

x= 240/0.02 = 12,000 . . . . amount invested at 4%

21,000 -x = 9,000 . . . . . . . . amount invested at 2%

The amount invested at 2% is $9,000.

The amount invested at 4% is $12,000.

_____

<em>Comment on method of solution</em>

These problems can usually be solved using one variable for the amount associated with the highest contribution to the mix. Here, that is the amount getting 4% interest. This keeps the numbers in the solution positive, helping to minimize errors. As you can see, the solution develops in about 2 or 3 steps. Other methods can take longer.

inysia [295]3 years ago

6 0

Answer:

$12,000 at 4%

$9,000 at 2%

Step-by-step explanation:

If x represents the amount invested at 4%, then the total interest earned is ...

0.04x + 0.02(21000 -x) = 660

0.02x = 240 . . . . . . . . . . . simplify, subtract 420

x= 240/0.02 = 12,000 . . . . amount invested at 4%

21,000 -x = 9,000 . . . . . . . . amount invested at 2%

The amount invested at 2% is $9,000.

The amount invested at 4% is $12,000.

_____

Comment on method of solution

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Step-by-step explanation:

We have to find the point in the feasible region which maximizes the objective function. To find that point first we need to graph the given inequalities to find the feasible region.

Steps to graph 3x + y ≤ 12:

First we graph 3x + y = 12 then shade the graph for ≤.

plug any value of x say x=0 and x=2 into 3x + y = 12 to find points.

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Similarly plugging x=2 will give y=6

Hence second point is (2,6)

Now graph both points and joint them by a straight line.

test for shading.

plug any test point which is not on the graph of line like (0,0) into original inequality 3x + y ≤ 12:

3(0) + (0) ≤ 12

0 + 0 ≤ 12

0 ≤ 12

Which is true so shading will be in the direction of test point (0,0)

We can repeat same procedure to graph other inequalities.

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Since objective function is not given in the question so i will explain the process.

To find the maximum value of objective function we plug each corner point of feasible region into objective function. Whichever point gives maximum value will be the answer

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