A
Date: _ _ _ __
PreAlgebra
Name:
t1 Swel ,/(,,{
Equations - Solving Word Problems
Sheet # 05-08
STllATICY: CLUE in to KEY WORDS!
Focus on key words as clues to setting up equations.
A pair of shoes costs $25. This is $14 less than the
cost of a pair of jeans.
PART A Define a variable.
Let
i :::
J
cos~ af jeaos.
Amy has saved $725 for a new guitar and lessons.
Her guitar costs $475, and guitar lessons are $25
per hour. Determine how many hours of lessons
she can afford.
PART A Define a variable.
Let
PART B Write an equation that can be used to solve for the
variable.
Equation
d5 ::
J -14
Ji : -:#.of hoors
PART B Write an equation that can be used to solve for the
variable.
,I
Equation
PART C Solve the equation to find the cost of a pair of
jeans.
f- J 5 =7 ':f 5 f 2 5
~
Part C Solve the
fj
!
2<:
h""::
-jq
-----
Answer$
FINANCIAL LITERACY
The cost for a certain music plan is $9.99 per year
plus $0.25 ~song you download. If you paid-- ·
$113. 74~ find the number of songs you
downloaded.
n
p ART A Define a variable.
Let
d=# of downloads
Equation
I(}
------'---
hours
Trey went to the batting cages to practice hitting.
He rented a helmet for $4 and paid $0.75 for each
group of 20 pitches. If he spent a total of $7 at the
batting cages, how many groups of pitches did he
pay for?
Let
solv~
for the
,1 "'I
q• / -J- 0.!_5 ~ j-::; I 1t Ji;/
Qq
-
Answer
PART A D.efine a variablef
PART B Write an equation that can be used to
variable.
I0
Part C Solve the word problem using your equation.
g 9'DUJ?-5 n pJches .
0
PART B Write an equation that can be used to solve for the
variable.
Equation
J
4 ./- "15 == q
Part C Solve the word problem.
e~c:·,_1 ~
.. :rs ! .~1~
_5___ songs
Answer __4_/
3~4
Answer ___1__,___ _ groups
ftUTIGY: Picture Perfect Problem Solving!
Try drawing pictures to help you create the equations.
From ground level to the tip of the torch, the Statue
of Liberty and its pedestal are 92.99 meters tall.
The pedestal is 0.89 meter taller than the statue.
How tall is the Statue of Liberty?
Jx
92. I
2
PERSEVERE WITH PROBLEMS The ages of three
siblings combined is 27. The oldest is twice the age
of the youngest. The middle child is 3 years older
than the youngest.
Write and solve an equation to find the age of each
sibling.
~1.~~(~j
~~zC/-
4 X +3 1= ;) t
x
O/de1 f ~ 6
-ft-::: / 2
. __. ~:~..11-.:::dl._ mJJ fe t; f 3 :;; q
I
The length of each side of an equilateral triangle is
increased by 5 inches, so the perimeter is now 60
inches.
Write and solve an equation to find the original
length of each side of the equilateral triangle.
I
__":J.x_::: )?el
...,
--·
x b"j,
1/t/Un t.i ::. t;;
!'
J
Anne bought a
necklace for each of her three sisters. She paid
$7 for each necklace. Suppose she had $9 left.
Write and solve an equation to find how much
money Anne had initially to spend on each
sister.
REASON ABSTRACTLY
3 (x+s)f Go
t -
3
I
q
X t 5:: .2.D
-5
-5
~
x
Derek and Madison work at a veterinarian's office
cleaning tJJe animal cages. There are 14 cages, and
each day Derek cleans 4 more cages than Madison
does. How many cages does each person clean?
- 1·3
=
x -t2.I
21 :q
42,I
q
~
Mr. Singh had three sheets of stickers. He gave 20
stickers from each sheet to his students and has 12
total stickers left.
Write and solve an equation to find how many
stickers were originally on each sheet.
x
x
-20
~zo
.. I 2
3 (X -Jo) ::_g
····~-
3
3
x--zn :: 1
+2
{'20
x :;. ;t_'-/
u
x
-z
----·---·-1'
Name:
Af\S'N{' <l. Yu
tt
Date:
PreAlgebra
-----
J
Equations - Solving Word Problems
It costs $13 for admission to an amusement park,
plus $1.50 for each ride. If you have a total of
$35.50 to spend, what is the greatest number of
rides you can go on?
-i
+I 50 I'
3
Sheet # 05-09
REASON ABSTRACTLY Elsie would like to take
snowboarding lessons at Powder Mountain. She
has save.d.$55.Q for lessons and a junior season
pass~~~-or~i-private lessons than
private lessons sfie can take?
so
PiW'det1Mowtain·,src;,aillnit •< ·. •
"···.·~.
Semf-Pnvate
I $45/lesson
1
••
•
. ·. _::c• ...•• i~nt!W~~l!dtfl"g3_~&C)'~l)
----~-------~---------~---
$£0/lesson
Private
·---------·----->--------{
5-3
0
J5
When diving, the peregrine falcon can reach
speeds of up to 17~ __rllilesper hour.
PART A
The top speed of a peregrine falcon is 20 miles per hour
~three times the top speed Of a cheetah. What is the
cheetah's top speed?
}?Tl5+
f
0
/:J5~•3c--
o
-t2o
!'I~
I '1 "J
fil: 23f
"ts
··'-ft"
J:: ;f5;2
!'5 f!s;s,si;,.l\)
The table shows the number of baseball cards in
two baseball collections. If Marcus and James have
120 cards altogether, write and solve an equation
that could be used to find the number of cards in
I
Marcus' collection.
+20
•. ?
:;;C
~-
3"3
b(
/-3ff
-31)
I
rp f 3C
45J2..:::/550
,,
PARTB::: (..
A sailfish can swim up to 1 mile per hom(re·s.stha9Jone-fifth
the top speed of a peregrine falcon. Find thelop-speed that
a sailfish can swim.
·1
l·····-··········--··--···+········-····-··-········j
James
2m
+6
12 0
1
I
3 ('(\ -1- (Q
-lo
~··--·~·"~~•"""'",,,..."'""
.... ~""'°"'",_,,.
3m
2·~
\ a
-6
""""•N•T•~~,,_ • .,,,,~,..
=114-
-=J 3
m::: 3~
-fZ =~ rp -I
{'.:: __J....
T
5
In a recent NfLgame,Jhe Green Bay Packers
scored 14 p6}11t§J_~_§§Jh<tl)Jl::te Tennessee Titans.
Write and solve an equation to find the total points
the Tennessee Titans scored.
(115) ~-1
...
l
f:; 3 5-J
PARTC
The peregrine falcon can reach speeds about 13 miles per
hour i;nt5fe t-~~ ti~es the speed of the fastest human.
Whatlsifie approximate top speed of the fastest human?
rp ,.
f 15
13 -I-
13 ~I-
Gh
h
Titans
p
MAKE A CONJECTURE
Hunter and Amado are each trying to save $600 for
a summer trip. Hunter started with $150 and earns
$7.50 per hour working at a grocery store. Amado
has nothing saved, but he earns $12 per hour
painting houses.
PART A Make a conjecture about who will take longer to
save enough money for the trip. JUstizyyouFreasO'fifng:"
(m oo'I a osw~ <.~
o <'ce r le J ]
\> )l +i : ;:
f_. .
Which pair of operations should you use to solve
p(x-q) = r for x?
_
: : ..... }.II
y Multiply by p. Subtract q.
tt:) ~ p
y Multiply by,1. Add q.
··. .o( y -<i_) ~ r
C Divide by P_;,Subtract q. -~:----
tr Cr
.:>
J
P...
/1)\ Divide by p. Add q.
9
Kimberly needs $5 to go the amusement park.
She has $13. She earns $8 per hour working at
her job. The equation 8h + 13 = 45 shows this
relationship. How many hours does Kimberly
need to work to earn enough money to go to 1
MULTIPLE REPRESENTATIONS Miguel and
three of his friends went to the movies. They
originally had a total of $40. Each boy had the
same amount of money and spent $7.50 on a ticket.
How much money did each boy have left after
buying his ticket?
MODEL - Figure out the problem using pictures or
diagrams.
Lx-~·JEljj
Lx I1\1) l L~Jl:i!I
L~1~~7
~-~
4 {) 1 fbolf :;· '3{) _40
3e
\w•
10·&:4=@ -rQ
ALGEBRA - Write and solve an equation that represents
the situation. L~-222
= 40
the park?
A
B
8
C
@)
7
6
4
/''•
fl
L((/()tl'j
"6
got oJI ~i\CQ.,
~ {\\~.$
s r-e·"+ jt i 1
3
e algebraic
() ,, 1 Wew'S J
Both qave Jlt., s<WB
8\-\ :: g
Each week, Payat spends a portion of his
allowance to download music. The table
shows th cumulative
ount that he spent on
music downloads during a three-week p~riod.
3
2
solution
41\
··13
@
':Jf\
COMPARE the arithmetic solution an~
1'
~·
ix:.ll\
~-1.
go h + I.}
- 1f3
x- :::('
A company employ$' 72 )Yorkers. It plans to
increase the number 'O!employees by J5 ~r -) G iY1
month until it has_!_,~i~~ its current workforce.J ·'1--~
·Wlilch equation caiioe used to determine m,
the number of months it will take for the
number of employees to double?
A 6m+72m=l44 C 2(6m+72)=144
B 2m + 72 = 144
6m + 72 = 144
n\€011s
(la<.;~~ I f.ktJ
:+~11 a.lqebt~1c we.if fitliett bi.l
k
~b.l\'4$.,
36
At the end of Week 3, Payat had $9 left.
Which equation can be used to find the amount
of Payat's weekly allowance a?
3(a-12) = 9
C 3(a + 12) = 9
B
9(a + 12) = 3
D
9(a-12) = 3
©
"'
ti