Spring 2016 Math 166
3. Write and solve (using rref) a system of
equations for the following problems:
Week in Review X
courtesy: David J. Manuel
(covering Sections F.4, 4.3-4.4)
1
Section F.4
1. You buy a home for $220,000, putting
10% down and mortgaging the balance
at 3.8% per year compounded monthly
for 30 years.
(a) What are your monthly payments?
(b) Show an amortization schedule for the
rst 2 months' payments:
Month Payment Interest Principal
0
1
2
(c) Once your loan is paid o, how much
have you paid total on the house?
(d) What is the equity in the home after 15
years?
(e) How much of the last payment of that
15 years goes toward principal?
2
Section 4.3
1. Write the system of equations below
in matrix form and use Gauss Elimination to solve:
3x + 8y = 4
15x + 10y = −10
2. Write the system of equations below
in matrix form and use Gauss Elimination to solve:
2x + 4y − 10z = −2
3x + 9y − 21z = 0
x + 5y − 12z = 1
1
(a) A manufacturing plant makes 3 types
of inatable boats: one-person, twoperson, and four-person models. Each
one-person boat requires 30 minutes cutting, 36 minutes assembly, and 12 minutes packaging. Each two-person boat
requires 60 minutes cutting, 54 minutes assembly, and 18 minutes packaging. Each four-person boat requires 90
minutes cutting, 1.2 hours assembly, and
0.5 hours packaging. If each week the
company has 380 labor-hours available
for cutting, 330 labor-hours for assembly, and 120 labor-hours for packaging,
how many of each type of boat should
be produced each week?
Balance
(b) A chemical manufacturer wants to lease
a eet of 24 railraod tank cars with a
combined carrying capacity of 520,000
gallons. Tank cars with capacities of
8,000 gallons, 16,000 gallons, and 24,000
gallons are available. Monthly costs for
leasing each type are $450, $650, and
$1,150 respectively. The manufacturer
has budgeted $24,100 for leasing costs.
How many of each type of car should be
leased?
(c) A dietician in a hospital is to arrange
a special diet composed of three basic
foods. The diet is to include exactly 340
units of calcium and 180 units of iron.
The number of units for each ounce of
the foods are summarized in the table
below:
Units
per
ounce
Food A Food B Food C
Calcium
30
10
20
Iron
10
10
20
If, in addition, the diet must consist
of twice as many ounces of Food C as
Food B, how many ounces of each food
should be used?
3
Section 4.4
1. Solve each of the following systems of
equations using any method. If there
are innitely many solutions, give the
general solution and two particular solutions:
(a)
2x − y − 3z = 8
x − 2y = 7
(b)
3x − 4y − z = 1
2x − 3y + z = 1
x − 2y + 3z = 2
(c)
2x − y = 0
3x + 2y = 7
x − y = −1
(d)
3x − 2y + z = −7
2x + y − 4z = 0
x + y − 3z = 1
2. A corporation wants to lease a eet of
12 airplanes with a combined carrying
capacity of 220 passengers. The three
available types of planes carry 10, 15,
and 20 passengers respectively. How
many of each type of plane could be
leased?
2