Systems of Linear Equations: Word Problems Name__________________
There are 3 main formats for the systems you will be asked to write on your Unit 7 test. (These are not all the formats for linear systems, but are the only types
on the test.)
TYPE 1: problems with two initial amounts TYPE 3: problems with two combinations
and two different rates TYPE 2: problems with a set number of and two totals
y = mx + b things, a total and two given rates Ax + By = C
y = mx + b x+y=D Dx + Ey = F
TYPE 1 EXAMPLE: The volleyball team is Ax + By = C
trying to book a location for their banquet. TYPE 2 EXAMPLE: Marc sold 461 tickets for TYPE 3 EXAMPLE: At a garden shop, a
The Blue Room restaurant quoted a price of the school play. Student tickets cost $3 and customer pays $48 for 5 geraniums and 4
$380 for the room and $20 a person for the adult tickets cost $4. Marc’s sales totaled
lilies. Another customer pays $58 for 4
dinner, while Green Acres quoted a price of $1624. How many adult tickets and how
$30 per person. How many people would many student tickets did Marc sell? geraniums and 6 lilies. What is the cost of one
have to attend in order for both restaurants geranium and one lily?
to cost the same amount?
Type 1 Problems
1.) Rite Rug charges $4 per square foot for carpeting and $95 for installation. Lowe’s charges $6 per square foot for carpeting and $75 for installation. Find the
square footage and price for which the total cost is the same for each store.
2.) Capri Lanes charges $2.25 per game for bowling and $2 for renting a pair of shoes. Larry’s Bowling Alley charges $2.75 per game and $1 for shoe rental.
Find the number of games played and the amount spent for which the total cost is the same at each bowling alley.
3.) A new fitness club recently opened in town causing membership at the old YMCA to drop. At the time when the new club opened, there were 100 people
that pre-registered and each week an average of 7 new members joined. When the new fitness club opened, there were 573 members of the YMCA and each
week since, enrollment has decreased by 3 members. After how many weeks will the total number of members for each fitness club be the same?
Type 2 Problems
4.) For a floral arrangement class, Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects. Each twig cost $1.00 and each flower
costs $3.00 and she spent a total of 15.00 on the twigs and flowers. Find the number of twigs and the number of flowers she used.
5.) Mr. Dewese bought a total of 20 pounds of grass seed at his local nursery for $168.00. He paid $9.00 per pound for Kentucky bluegrass and $6.00 per
pound for Tall Fescue. Find the number of pounds of Kentucky bluegrass and Tall Fescue Mr. Dewese bought.
6.) SMS library is having a book sale to raise money. Hardcover books cost $4.00 and paperback books cost $2.00 each. A person spends $26 for 8 books. How
many hardcover books did the person purchase?
Type 3 Problems
7.) Joe bought 4 hot dogs and 4 sodas at the baseball game and paid $20. Karen bought 2 hot dogs and 3 sodas and paid $12. What is the cost of one hot dog at
a baseball game? One soda at a baseball game?
8.) Two families went skiing on Saturday. One family purchased two adult lift tickets and four youth tickets for $166. Another family purchased four adult lift
tickets and five youth tickets for $263. How much would it cost two adults and five youths to ski for a day?
9.) Q-Mart was having a sale on shirts and pants for Groundhog’s day. Walter spent $129 on 5 shirts and 2 pairs of pants. His friend Greg spent $224 for 8
shirts and 4 pairs of pants. How much did each pair of pants cost?
10.) Eldora and Finn went to an office supply store together. Eldora bought 15 boxes of paper clips and 7 packages of index cards for a total cost of $55.40.
Finn bought 12 boxes of paper clips and 10 packages of index cards for a total cost of $61.70. Find the cost of one box of paper clips and the
cost of one package of index cards.
11.) Cadence has a collection of 52 dolls that all have either blue eyes or green eyes. Cadence has 16 more blue-eyed dolls than green-eyed dolls. Find the
number of each type of doll.
12.) Dalton has 7 bills, all tens and twenties, that total $100 in value. How many of each bill does he have?
13.) Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of
lemonade and collected a total of $265, how many cups of each type did he sell?
14.) Susanna is packaging a blend of mixed nuts and candies for wedding favors. The mixed nuts cost her $3 per pound and the candies cost her $4 per pound.
Susanna spends $27 on 8 pounds of nuts and candies. How many pounds of nuts were in the mix? How many pounds of candies?
15.) A rental car agency charges $15 per day plus $0.11 per mile to rent a certain car. Another agency charges $18 per day plus $0.08 per mile to rent the same
car. How many miles will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency?
16.) Two trains leave a train station at the same time heading towards each other. The train that left from Bellingham is traveling 60 miles per hour. The
train that left from Seattle is traveling 72 miles per hour. If Bellingham and Seattle are 90 miles apart, how many minutes will it take before the trains pass
each other? How far from Seattle will they be?
17.) Kristen and Janaka are decorating their friend’s locker for her birthday. They both buy balloon bouquets made up of regular balloons and shiny Mylar
balloons. Kristen spends $13 for 5 regular and 2 Mylar balloons. Janaka spends $20 for 6 regular balloons and 4 Mylar. What is the cost of each regular
balloon? Each Mylar balloon?
18.) A catering company is setting up tables for a big event that will host 764 people. When they set up the tables they need 2 forks for each child and 5 forks
for each adult. If the company ordered a total of 2992 forks, how many adults and how many children will be attending the event?
19.) Lakota bought 6 new compact disks and 2 used compact disks for $127.92. Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89.
Find the cost of buying a single used compact disk.
20.) Juanita and Keenan own a camping supply store and just put in an order for flashlights and sleeping bags. The number of flashlights ordered was five
times the number of sleeping bags. The flashlights cost $12 each and the sleeping bags cost $45 each. If the total cost for the flashlights and sleeping bags was
$1785, how many flashlights and how many sleeping bags did Juanita and Keenan order?
Challenge Problems (Other Forms)
21) A group of 52 people attend a ball game. There were three times as many children as adults in the group. How many children were in the group?
22.) Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the
number of 30¢ stamps. How many stamps of each kind did Galina buy?
23.) Ilida went to Minewaska State Park one day this summer. All of the people at the park were either hiking or bike riding. There were 178 more hikers
than bike riders. If there were a total of 676 people at the park, how many were hiking and how many were riding their bikes?
24.) The sum of the ages of Petra and her mother is 53. Her mother is 11 years more than twice as old as Petra. How old are Petra and her mother?
25.) A drummer is stocking up on drum sticks and brushes. The wood sticks he buys are $10.50 a pair and the brushes are $24 a pair. He ends up spending $90
on sticks and brushes and buys twice as many pairs of sticks as brushes. How many pairs of sticks and brushes did he buy?
26.) How many spheres would it take to balance one cube?