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40. solve the system of linear equations using the Gauss - Jordan elimination method
2x + y - 2z = 4
x + 3y - z = -3
3x + 4y - z = 7
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|Solution: x = 6, y = -2, z = 3 |
52. Investments: Michael Perez has a total of $2000 on deposit with two saving institutions. One pays interest at the rate of 6% year, whereas the other pays interest at the rate of 8% year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposit in each institution?
|Let the investment at 6% be x and that at 8% be y. Then we can form the following equations: |
|x + y = 2000 |
|(6/100)x + (8/100)y = 144 |
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|Solution: x = $800, y = $1200 |
57. Investment Planning: The annual returns on Sid Carrington's three investments amounted to $21,600: 6% on a saving account, 8% on mutual funds, and 12% on bonds. The amount of Sid's investment in bonds was twice the amount of his investment in the savings account and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment.
|Let the deposit in Savings account be x, that in Mutual funds be y and in Bonds be z. Then we can form the following equations: |
|(6/100)x +(8/100)y + (12/100)z = 21600 |
|z = 2x, that is 2x - z = 0 |
|(12/100)z = (8/100)y, that is 8y - 12z = 0 |
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|Solution: x = $40000, y = $120000, z = $80000 |
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