Liam wants to buy a car and pay for it in three installments. The total cost of the car is $29,000. Two times the first installment is $1,000 more than the sum of the third installment and three times the second installment. Liam must pay 15% interest on the second and the third installments: the interest will amount to $2,100. If x, y, and z represent the first, second, and third installments, respectively, identify the augmented matrices that model Liam's situation.

Question

Mathematics

Kaitlyn Leach

20 February, 19:30

Liam wants to buy a car and pay for it in three installments. The total cost of the car is $29,000. Two times the first installment is $1,000 more than the sum of the third installment and three times the second installment. Liam must pay 15% interest on the second and the third installments: the interest will amount to $2,100. If x, y, and z represent the first, second, and third installments, respectively, identify the augmented matrices that model Liam's situation.

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Answers (1)

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Jazz · Answer 1

X + y + z = 29000

y = 3x

z = (2x - 1000)

x + 3x + (2x - 1000) = 29000

6x - 1000 = 29,000

6x - 1000 + 1000 = 29000 + 1000

6x = 30000

6x / 6 = 30000 / 6

x = 5000

x = 5000

y = 3x = 3 x 5000 = 15000

z = (2x - 1000) = 2 x 5000 - 1000 = 9000

x + y + z = 29000

5000 + 15000 + 9000 = 29000