MATH 95
Name:
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Fall 2016
Test 3
****Show all work. Correct Solutions without work will be given no credit.****
1. Solve the system of equations by graphing:
-6x- 3y = 9
{ 4x + 2y = 4
tIJ
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w.
-ftJX- ?;'/: ~
2.x +'j -: :.
-3
4x+2'f = lf
2x+'J=2.
'I:.- 2x+- 2.
'j::. -2.x- 3
m:-2..
yY'\-:. -~
'I ,Y\'krttf~ =( o, '2-' )
\1''n~t -:. {o,-~)
1
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t
2. Solve the following by substitution or elimination:
(a) { 3x - 5y = 1
2x- y = -4
?.>x -7:>'( -= l
~.'X -
'j =-l\-
~
5x-Sy:\
""'"-l 0')( +5'( = 2..0
-+x : 2.\
X~ 2
'
-1
=-3
x=--3
'2.x ...~:-Y.
~( -~) -~ ~- y.
-~ ~-'++6
-~: :2..
~~-2-
Lc-3,-2)]
" 3t-3) - ~l-2) :. -C, + \0-=- \
./
.2t ~)- (-2) -:. -tot 2--- Lt- /
2
(b) { 3x - 8y = -2
4x- 7y
=1
3x-S~ =-2 _...., - \2.x +-~~L\:
8
..J
~'>< - '+-'j = I
+ \ '2x -2.\~ :: '!:>
\\'j= 11
~
4 x-1-~
=\
4x -t-£1) ='
4x
l++
==
4x=%
"~!..:2.
4
J
3 ( -i) - <istJ') -:.
"-)so ': -2.
v 4(i) -+-lll ': 8 -1-= \ ./
3
=\
~.i.'.ljr~h 5y-2.x: lC
3. Graph the solution set to 5y - 2x < 10
10
1
sy=
~ 't
2.~~ to
'1; ~x+.2
~~: rY\(Att ~~!lN..'~ dlb)46l
4
~ ~e.V\o-\t.
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-
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4. G
{ ~~h the solution set to
3
x+ y ;::=: 2
4
£_ '
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5. Choose three of the following word problems to solve. You MUST solve using a system
of equations.
(a) A fruit company delivers its fruit in two types of boxes: large and small. A
delivery of 2 large boxes and 5 small boxes has a total weight of 105 kilograms.
A delivery of 6 large boxes and 3 small boxes has a total weight of 99 kilograms.
How much does each type of box weigh?
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2 ')( t- sy
~~ +-
= \OS
?;y :: qq
-Cox-\ sy ~ -~\ s
-r
~X+
3t :-: qq
-\'l'f ~ -.2\~
'/-=- \e
~ ~sMill...bo~
2x 'rsy :; 'os
~XT'Sl\~~ ~lOS
.:2x ~ \O'j- "! 0
;).x, :: l "5
)< ::
~
:
':f
i
k~
-(V \~e. bl)L
':} i. ~ ~ e~c.h Ia.~ box
1e ~ -fv'- t.o..th snt.&. bax
(b) A nurse is going to mix a 25% salt solution wit h an 45% salt solution. She needs
to make 180 milliliters of a solution that is 30% salt. How much of the 25% and
45% solutions are needed?
Le.4- X~
#mL..
o+- 2 S~o
tj ;:- 4tmL o.P 4SC?o
'X+'/ = \ f>C
sc&..t so\\.\.i'·~
~ so\t.t."'M
X+'J =\~
-=)
:~. "::>x ~ •'+5'{ -:. •3o Uso)
~ '5 ')( +'-+'5 ~ =5 4-0
'X -\-~ ::-l C60
'{: \tO-)<.
d'S X...- q.S[ \~e-X) =BlfcrO
QC:, X
+ ~\ 00- "\-~')(
-~O)(-::.
"= '5 4.00
-:lT-00
X=- - 2 +oo
-'J..O
. . \ ~S
-
x+~=lfsb
fo~+~ =t~a
~ ::45YV\L lf'"=>"o
\ ~ 5 Y't'\Lert .:<~1· 56..-\+ solu."h~
4 S M L e .C 4 'SII)~ ~i- .Q, h..t.i\.0>'\
6
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(c) Flying against the wind, an airplane travels 6400km in 8 hours. Flying with the
wind, the same plane travels 9100km in 7 hours. What is t he rate of the plane in
still air and what is the rate of t he wind?
L.e. +-
X:, ~'t!-o~ flAAt
'\ n ~"\\· \l ~~
~ :: f""oJt ~ W\nei\ CUft'V\ +R-· T-:::D
~x ...
e1 :: ~4oo
7x +~ =-ct 1oo
X-~ =~00
-7
+ X '+-'1 :
1'"300
;<x-::.~loo
X:;~= \oSO
,_
~-~ =-~0
'6?0 ... '{:-tOO
-y ~ -:2_50
~:~SO
r-tA.'ft. 0.p. pto.JH~. :. (0 ~0 k:.M/ \+fL
~
0
.f
\)J
\V\C(_ ~
'l~ 0 ~M j f+{1...
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(d) Donna had $20,000 to invest. She invested some of it in an account t hat paid
10% simple interest per year, and she invested the rest in an account that paid 5%
simple interest per year. After one year, she received a total of $1950 in interest.
How much did she invest in each account?
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X-+-Y
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=2o ooo
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1
X+i: 2o,ooo
toxt- sy-=-
'I ='l.opoo -'X
=l '\~,ooo
\0 X+ \00 000- Sx =lq ~ ,oOO
lo~t- st~}:oo-x\
1
S.x = '1'S I ooo
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= 'ls,ooo
:::.; \ q~ooo
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~l'l,ooo +j 1''2.o,r:t:J:J
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