Intermediate Algebra
Name
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Chapter 4.3: Solving Applications of Systems of Linear Equations in 3 Variables 0
1. Say you went out trick-or-treatmg and received 24 pieces candy. The number of Tootsie-Pops you got is
two less than twice the number of pieces of Snickers. The number of Starbursts is two more than five
times the number of pieces of Snickers. How many pieces of Snickers, Tootsie-Pops, and Starbursts did
you get?
Let
u - \i)sMx(h
Tcc\-ili A^y^
Equation 1:
Xtdrt^^^H
Equation 2:
U x '2JC'X
'
t^^^^.
Equation 3:
6
Answers: 3 = number of Snickers
4 = number of Tootsie-Pops
17 = number of Starbursts
2. A 141-person crew is made up of inspectors, contractors, and laborers. The number of contractors is four
more than the number of inspectors. The number of laborers is three less than eight times the number of
inspectors. Determine the number of inspectors, contractors, and laborers on the crew.
Let
\iicx\V>tA
i;r\fi>^cx(A
Let
- Vy\jiWKif\V \rxLetjL_i\
Equation 1:
Equation 2:
Equation 3:
KiU^^
^
u „
>CV^
_*
>
^
\VI-5
Answers: 14 = number of inspectors
18 = number of contractors
109 = number of laborers
3. At local stationary store 3 notebooks, 2 pencils, and 4 pens are sold for $6.13; 2 notebooks, 5 pencils,
and 3 pens are sold for $5.50; and 1 notebook, 3 pencils, and 2 pens are sold for $3.12. What is the price
of 1 notebook, 1 pencil, and 1 pen sold individually?^ [
Let
•
=
L e t ^ =
I (H r\
(Aitl
CV^ f\ s^ir\\
Let
'
Equation 1:
••
'
' ^
Equation 2: 2 X - ^ 5 ^ i \ % ^
^'^f-^'^
6
Answers: $1.29 = the cost of 1 notebook
$0.35 = the cost of 1 pencil
$0.39 = the cost of 1 pen
_
^
"
9'3.-V-^i7
^-"^ ^ x .
C\^^'CJf^»
4. A vendor at a rock concert needed tolceep t r a c ^ f the number of long-sleeve shirts, short-sleeve shirts,
and tank-tops he sold at the concert, which sell for $16.99, $14.99, and $12.99, respectively. He
completely forgot to keep track, but he knew he could figure it out. The register tape revealed that a
total of 167 shirts were sold, which brought in a total of $2477.33. He also could tell from the empty
boxes that he sold 7 more short-sleeve shirts than he did long-sleeve. How many shirts of each type did
the vendor sell?
L e t =
iWisvbv c\
Let U =
&\r
Let ^ - \^ViMlf C
AcT^rY^^.
Equation 1:
Equation 2:
Equation 3:
^tH'^'^ .?>3
\bA^)Cr Hft^U^"^
1^ " "
Answers: 49 = the number of long-sleeve shirts sold
56 = the number of short-sleeve shirts sold
62 = the number of tank-tops sold
^^-^
Hf^^^C*^'
ESQ
5. A candy store owner needed to keep track of the number of 1-ounce bags, 2-ounce bags, and 3-ounce
bags of candy he sold during the week, which sell for $0.99, $1.09, and $1.29, respectively. He
completely forgot to keep track, but he knew he could figure it out. The register tape revealed that a
total of 43 bags were sold, which brought in a total of $47.57. He also could tell from the depleted
candy barrel that he sold a total of 81 ounces of candy. How many bags of each size did the owner sell?
Let
Let
Let^
Equation 1:
^
Equation 2:
)<^VVvW^
^ C f ^ f (^OqU
\)C-V
M 2>
^^'^^'h =
"ffcS?
Z L ^ V i ^ , - fc\
Answers: 17 = the number of
.f 1-ounce
1 -ouncebags
bass sold 1 ^
14 = the number of 2-ounce bags sold
12 = the number of 3-ounce bags sold
yCS'" 1
-^
6. A local bakery sells three kinds of cookies: chocolate chip cookies at 15^ each, oatmeal cookies at 20*^
each, and peanut butter cookies at 25^ each. Say you buy some of each kind and choose three times as
many peanut butter cookies as chocolate chip cookies: If you spent $4.10 on 19 cookies, how many of
each kind did you buy?
L e t J C - \\}^W\)XX CV\(><.
(Ut\
i-ir^
Let ^
= \W^X<
oV Odkm:rA
Let
Equation 1:
4,10
^ \ C : ^ ^ J £ ^ ^ /j^yt^^
Equations: ^ ^ • ^ ^ . . ^ ^ ^ ^ C ^ . ^ ^ ^ X C ^ ^ ^ ^ . ^ . C
Equation 2:
Answers: 3 = the number of chocolate chip cookies bought
7 = the number of oatmeal cookies bought
9 = the number of peanut butter cookies bought
\X.^_3V
7, Say you invested $70,000 into three accounts: part at a 2% simple interest rate, part at a 10% simple
interest rate, and the remainder at a 6% simple mterest rate. The amount of money invested at 10% was
twice as much as the amount invested at 2%, How much do you have invested in each account if the
total interest gained on all three accounts in one year wa§,$4800?
/
X = A^tKH
Let
Let
a
Let
/
VxW£:^^d
a\
-mjs^
-
^
^ ^
&l
Equation 1:
)C V U ^ ^ - ^^QXC^
Equation 2:
i i „ 2%-
Equations:
^^^^^.^^^^^^g^
4
—~
o4^=(^cc
"
•-
•J
Answers: $15,000 = the amount of money invested at 2%
$30,000 = the amount of money invested at 10%
$25,000 = the amount of money invested at 6%
8. A 12% solution, a 14% solution, and a 30% solution of sulfuric acid are to be mixed to get 12 liters of a
20% solution. How many liters of each must be mixed if the volume of the H%o solution must be 2 liters
less than the volume «f the 3*3% solution?
L e t =
OJ
L e t ^ =
i^^VKuOV
Equationl:
Equation 2:
h / i
^fA^
)^V\\V^^^2-
^
Equation 3:
.02*-
. 2 ^ -.©"j
=^ *
-"2Answers; 4 liters = the amount of 12% solution
3 liters = the amount of 14% solution r-^~rS~v, /
5 liters = the amount of 30% solution \
y ^ - U - ^ - ^ ^ ^