Using Matrices, solve the following: A practical Humber student invested 20,000 in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was $1,880. How much does the student invested in each stock?

Anish Buchanan

Anish Buchanan

Answered question

2020-11-27

Using Matrices, solve the following: A practical Humber student invested 20,000 in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was $1,880. How much does the student invested in each stock?

Answer & Explanation

Sadie Eaton

Sadie Eaton

Skilled2020-11-28Added 104 answers

Step 1
Let x be the amount invested at 7%
y be the amount invested at 11%
Total amount invested = 20000
Thus, x+y=20000 ...(1)
Interest received at 7% =0.07x
Interest received at 11%=0.11y
Total interest received =1880
Thus, 0.07x+0.11y=1880 ...(2)
step 2
Hence we have two system of equations
x+y=20000
0.07x+0.11y=1880
we solve it by matrices
It can be expressed as
[110.070.11][xy]=[200001880]
Augmented Matrix for Ax=b is
[11200000.070.111880]
R2R20.07R1[11200000.070.111880]
Which can be expressed as
x+y=20000
0.04y=480
y=12000 And, x=2000012000=8000 Hence [xy]=[800012000]
Step 3
ANSWER:The student invested 8,000 at 7% interest and 12,000 at 11% interest
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

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