Math 141 Week in Review
Week 3 Problem Set Answers
1.
y=
2
4
x!
3
7
2.
n=
8
3
3.
A. $6
B. P ( x ) = 4 x !1500
C. 375 keychains
D. $2250
4.
1
A. Demand: p = ! x + 75
8
1
Supply: p = x + 15
4
B. (160, 55); 160 sleeping bags at $55 each
5.
A. y = 71.39x – 201
B. 1227 stores
C. 2012
D. r ≈ 0.9665. Since |r| is very close to 1, the line models the data very well.
6.
A. Yes; No Solution
B. No; !9R2 + R1 " R1
C. Yes; Exactly 1 solution
D. No; !R2 + R3 " R3
E. No; 13 R2 ! R2
F. Yes; Infinitely many solutions
7.
1
4
R1 ! R1
"1 2
$
#!3 !5
8 %
'
!18&
3R1 + R2 ! R2
!1 2
#
"0 1
8$
&
6%
!2R2 + R1 " R1
"1 0
$
#0 1
!4%
'
6&
The solution is (–4, 6)
8.
x = the number of Dr Peppers
y = the number of coffees
68x + 230y = 1830
250x + 130y = 3150
Jill drank 10 Dr. Peppers and 5 coffees.
9.
A. No Solution
B. Infinitely many solutions; (!t + 3,t !1,t )
10.
a = 8, b = –4, c = 21, d =
11.
B = [5 3 6] ; BA = [129 133]
John will spend $129 if he orders from Papa John’s and $133 if he orders from
Pizza Hut.
12.
A.
B.
C.
D.
E.
13.
A. x = the number of Southwest flights
y = the number of Delta flights
z = the number of American flights
1
2
Possible
Not Possible
Possible
Possible
Not Possible
135x + 160y + 148z = 88,683
x = 3y
z = 12 ( x + y )
"135 160 148%" x% "88683%
$
'$ ' $
'
!3
0 '$ y' = $ 0 '
B. $ 1
$# ! 1 ! 1
1 '&$# z '& $# 0 '&
2
2
"309%
$ '
C. X = A!1B = $103' ;
$#206'&
There were 309 Southwest flights, 103 Delta flights, and 206 American flights.
14.
!0.2 0.3 0.2$
#
&
A. A = #0.1 0.4 0.1&
#"0.1 0.3 0.3&%
!1700$
#
&
B. X = #1200&; 1700 units of agricultural products, 1200 units of transportation,
#"1050&%
and 1050 units of service.
"910%
$ '
C. AX = X ! D = $755' ; 910 units of agricultural products, 755 units of
$#845'&
transportation, and 845 units of service.