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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sqdancefan sqdancefan · Answer 1 · 2020-10-29T02:49:37+01:00

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Answer:

see below

Step-by-step explanation:

We assume the values of the installment payments are the values before interest is added. The given relations are ...

x + y + z = 29000 . . . . . . the total of the 3 installments is the price of the car

2x = 1000 +z +3y . . . . . . the 1st is $1k more than the 3rd and twice the 2nd

0.15(y +z) = 2100 . . . . . . 15% interest on the last two installments totals 2100

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We want to rearrange each of these equations to standard form:

x + y + z = 29000

2x -3y -z = 1000

0x + 0.15y +0.15z = 2100

Putting these coefficients into augmented matrix form, we have ...

[tex]\left[\begin{array}{ccc|c}1&1&1&29000\\2&-3&-1&1000\\0&.15&.15&2100\end{array}\right][/tex]

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The installments (before interest) are (x, y, z) = (15000, 7500, 6500) dollars.