MPM2D-01/03
Thursday, September 20, 2001
Solving Problems # 2 - Using Linear Systems
1)
A principal of $5000 is invested. Part of the $5000 is invested at 9% per annum,
the rest at 11% per annum. After 1 year, the total interest earned is $520. How
much money was invested at each rate?
ANSWERS
Let x represent the amount of money invested at 9 % per annum.
Let y represent the amount of money invested at 11 % per annum.
x + y = 5000
0.09x + 0.11y = 520
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $1500 at 9 % and $3500 at 11 %.
2)
A principal of $2100 was invested in the stock market. Some shares of World Oil
were bought at $7.50 per share. Some shares of Zinco Mines were bought at
$3.25 per share. The total number of shares was 450. How many shares of each
stock were bought.
ANSWERS
Let x represent the total number of shares of World Oil.
Let y represent the total number of shares of Zinco Mines.
x + y = 450
7.50x + 3.25y = 2100
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they purchased 150 shares of World Oil and 300 shares of Zinco Mines
Prepared by: Mr. McEwen
MPM2D-01/03
3)
Thursday, September 20, 2001
A principal of $500 is invested; part at 7% per annum and the rest at 10% per
annum. After one year, the total interest earned was $44. How much was
invested at each rate?
ANSWERS
Let x represent the amount of money invested at 7 % per annum.
Let y represent the amount of money invested at 10 % per annum.
x + y = 500
0.07x + 0.10y = 44
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $200 at 7 % and $300 at 10 %.
4)
A principal of $800 is invested; part at 9% per annum and the rest at 12% per
annum. After one year, the total interest earned was $79.50. How much was
invested at each rate?
ANSWERS
Let x represent the amount of money invested at 9 % per annum.
Let y represent the amount of money invested at 12 % per annum.
x + y = 800
0.09x + 0.12y = 79.50
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $550 at 9 % and $250 at 12 %.
Prepared by: Mr. McEwen
MPM2D-01/03
5)
Thursday, September 20, 2001
A principal of $2500 is invested; part at 8% per annum and the rest at 12% per
annum. In one year, the two investments earned equal amounts of interest. How
much was invested at each rate?
ANSWERS
Let x represent the amount of money invested at 8 % per annum.
Let y represent the amount of money invested at 12 % per annum.
x + y = 2500
0.08x = 0.12y
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $1500 at 8 % and $1000 at 12 %.
6)
A principal of $500 is invested; part at 9% per annum and the rest at 11% per
annum. After one year, the interest earned on the 9% investment was $20 less
than the interest earned on the 11% investment. How much was invested at each
rate?
ANSWERS
Let x represent the amount of money invested at 9 % per annum.
Let y represent the amount of money invested at 11 % per annum.
x + y = 500
0.09x + 20 = 0.11y
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $175 at 9 % and $325 at 11 %.
Prepared by: Mr. McEwen
MPM2D-01/03
7)
Thursday, September 20, 2001
Jim invested $3500, part at 15% per annum and the remainder at 10% per annum.
The total interest paid to him on his money in one year was $445. How much
money did he invest at each rate?
ANSWERS
Let x represent the amount of money invested at 15 % per annum.
Let y represent the amount of money invested at 10 % per annum.
x + y = 3500
0.15x + 0.10y = 445
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $1900 at 15 % and $1600 at 10 %.
8)
A man invested $6000, part of it at 4% and the remainder at 5% interest. How
much did he invest at each rate if he received $250 interest in one year?
ANSWERS
Let x represent the amount of money invested at 4 % per annum.
Let y represent the amount of money invested at 5 % per annum.
x + y = 6000
0.04x + 0.05y = 250
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $5000 at 4 % and $1000 at 5 %.
Prepared by: Mr. McEwen
MPM2D-01/03
9)
Thursday, September 20, 2001
Part of $2800 is invested at 5% and the rest at 6%. The annual income from the
6% investment is $52 less than that from the 5% investment. What amounts are
invested at each rate?
ANSWERS
Let x represent the amount of money invested at 5 % per annum.
Let y represent the amount of money invested at 6 % per annum.
x + y = 2800
0.06y + 52 = 0.05x
Using the Method of Substitution or the Method of Elimination you can find the
two numbers.
Therefore they invested $2000 at 5 % and $800 at 6 %.
Prepared by: Mr. McEwen