MATH 95
Fall 2016
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Test 3
****Show all work. Correct Solutions without work will be given no credit.****
1. Solve t he system of equations by graphing:
6x- 2y = 12
{ - 9x + 3y = 12
x
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-10
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fo-x -2. '/ -= I 2
t; 3x -'1: ~
-f1y..T3y =- 12.
4 -3x + 'f ='+
y: 3~
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'f ~ -~
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5LOPb= 3
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1
0
2. Solve the following by substitution or elimina tion:
(a) { 3x + 5y = 17
2x- y = - 6
3x-r5y-= I+
02x -
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3x+5y :.I :r
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'ox +-sy ~ -ao_
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-2 -':1 =-to
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1-=?
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(b)
{3x-
By= 7
lOx- 5y = 45
:3x-S~ =-:J
lox -sy: l.fS
4
30><- ~
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=+O
ttrsy =-\35
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3x-BLt) =+
3x -8 =- +
3x-=15
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{ :a~h the solution set to
3
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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 3 large boxes and 8 small boxes has a total weight of 97 kilograms. A
delivery of 5 large boxes and 2 small boxes has a total weight of 88 kilograms.
How much does each type of box weigh?
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ax +-'Oy =q-q.
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5
(b) A nurse is going to mix a 6% salt solution wit h an 11% salt solution. She needs
to make 370 milliliters of a solution that is 7% salt. How much of the 6% and
11% solut ions are needed?
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ro x + \ \ L-o -=10 ... ,>() =- 2. sq a
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6
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(c) Flying against t he wind , an airplane travels 5400km in 9 hours. Flying with the
wind, the same plane travels 7140km in 7 hours. What is the rate of t he plane in
still air and what is the rate of the wind?
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(d) Donna had $30,000 to invest. She invested some of it in an account that paid
7% simple interest per year, and she invested the rest in an account that paid 9%
simple interest per year. After one year , she received a total of $2440 in interest.
How much did she invest in each account?
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+ 'I
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'X +- \-:2- ''2..<60 = 30' ooD
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