Chapter 3 Word Problems – Choose to solve algebraically or
using matrices
1.)
You plan to work 200 hours this
summer mowing lawns and babysitting.
You need to make a total of $1300.
Babysitting pays $6 per hour and mowing
lawns pays $8 per hour. How many hours
should you work at each job?
2.) You enroll in a book club in which
you can earn bonus points to use toward
the purchase of books.
Each paperback
book you order costs $6.95 and earns you
2 bonus points.
Each hardcover book
costs $19.95 and earns you 4 bonus
points. The first order you place comes
to a total of $60.75 and earns you 14
onus points.
How many of each type of
book did you order?
3.)
A bus station 15 miles from the
airport runs a shuttle service to and
from the airport.
The 9:00 AM bus
leaves for the airport traveling 30 mph.
The 9:05 AM bus leaves for the airport
traveling 40 mph.
Write a system of
linear equations to represent distance
as a function of time for each bus. How
far from the airport will the 9:05 AM
bus catch up to the 9:00 AM bus?
4.)
The school yearbook staff is
purchasing a digital camera.
Recently
the staff received two ads in the mail.
The ad for store #1 states that all
digital cameras are 15% off. The ad for
store #2 gives a $300 coupon to use when
purchasing any digital camera.
Assume
that the lowest priced digital camera is
$700. When could you get the same deal
at either store?
5.) One evening, 76 people gathered to
play doubles and singles ping pong.
There were 26 games in progress at one
time. A doubles game requires 4 players
and a singles game requires 2 players.
How many games of each kind were in
progress at one time if all 76 people
were playing?
6.)
A citrus fruit company plans to
make 13.25 lb gift boxes of oranges and
grapefruits.
Each box is to have a
retail value of $21. Each orange weighs
0.5 lb and has a retail value of $0.75.,
while each grapefruit weighs 0.75 lb and
has a retail value of $1.25.
How many
oranges
and
grapefruits
should
be
included in the box?
7.) You are starting a business selling
boxes of hand-painted greeting cards.
To get started, you spend $36 on paint
and paintbrushes that you need. You buy
boxes of plain cards for $3.50 per box,
paint the cards, and then sell them for
$5 per box.
How many boxes must you
sell for your earnings to equal your
expenses?
What will your earnings and
expenses equal when you break even?
8.)
You ride an express bus from the
center of town to your street. You have
two payment options.
Option A: buy a
monthly pass and pay $1 per ride.
Option B: pay $2.50 per ride. A monthly
pass costs $30.
After how many rides
will the total costs of the two options
be the same?
9.) A soccer league offers two options
for membership plans.
Option A: an
initial fee of $40 and costs $5 for
each game played.
Option B: $10 for
each game played. After how many games
will the total cost of the two options
be the same?
14.)
An adult pass for a county fair
costs $2 more than a children’s pass.
When 378 adult and 214 children’s
passes were sold, the total revenue was
$2384. Find the cost of an adult pass.
10.) You worked 14 hours last week and
earned a total of $96 before taxes.
Your job as a lifeguard pays $8 per
hour and your job as a cashier pays $6
per hour. How many hours did you work
at each job?
15.)
A nut wholesaler sells a mix of
peanuts and cashews.
The wholesaler
charges $2.80 per pound for peanuts and
$5.30 per pound for cashews.
The mix
is to sell for $3.30 per pound.
How
many pounds of peanuts and how many
pounds of cashews should be used to
make 100 pounds of the mix?
11.) During one calendar year, a state
trooper issued a total of 375 citations
for warnings and speeding tickets. Of
these, there were 37 more warnings than
speeding tickets.
How many warnings
and how many speeding tickets were
issued?
16.)
You are on the prom decorating
committee and are in charge of buying
balloons.
You want to you both latex
and Mylar balloons. The latex balloons
cost $.10 each and the Mylar balloons
cost $.50 each. You need 125 balloons
and you have $32.50 to spend. How many
of each can you buy?
12.) A movie theatre charges $9 for an
adult’s ticket and $6 for a child’s
ticket. One Friday night, the theatre
sold a total of 848 tickets for $6711.
How many tickets of each type were
sold?
17.) A caterer is planning a party for
64 people. The customer has $150 to
spend. A $39 pan of pasta feeds 14
people and a $12 sandwich tray feeds 6
people. How many pans of pasta and how
many sandwich trays should the caterer
make?
13.) In
guitars
guitars
guitars
of each
18.) For spring break you a planning a
7 day trip to Florida. You estimate
that it will cost $275 per day in Tampa
and $400 per day in Orlando.
Your
total budget for the 7 days is $2300.
How many days should you spend in each
location according to your budget?
one week, a music store sold 9
for a total of $3611. Electric
sold for $479 each and acoustic
sold for $339 each.
How many
type of guitar were sold?