1. science
2. mathematics
3. algebra

6.4 – Word Problems (Day 1)
Objective: To write and solve a system of equations modeling real-life problems.
PROBLEM SOLVING
READ
PLAN
SOLVE
CHECK
 What do you know?
(make a list, chart, or picture)
 What are the key terms?
 What do you need to find?
 Represent the unknown
(define your variables)
 Set up equations
 Solve the equations
 Answer the problem
 Does the answer require units?
 Does the answer make sense?
Directions:
Read each situation. Define variables, set up a system of equations, and solve your system.
EXAMPLE 1: Mark and Christina each improved their yards by planting rose bushes and shrubs. They bought
their supplies from the same store. Mark spent $184 on 12 rose bushes and 5 shrubs. Christina spent $116 on 3
rose bushes and 10 shrubs. Find the cost of one rose bush and the cost of one shrub.
Let
x = ____________________
Equations:
y = ____________________
_______________________
________________________
EXAMPLE 2: A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 12
gloves were sold for a total revenue of $528. Right-handed gloves cost $48 and left-handed gloves cost $36.
How many of each type of glove sold?
Let
x = ____________________
Equations:
y = ____________________
_______________________
________________________
EXAMPLE 3: Ryan and Amar are selling cheesecakes for a school fundraiser. Customers can buy strawberry
cheesecakes and apple cheesecakes. Ryan sold 4 strawberry cheesecakes and 1 apple cheesecake for a total of
$30. Amar sold 7 strawberry cheesecakes and 1 apple cheesecake for a total of $48. Find the cost each of one
strawberry cheesecake and one apple cheesecake.
Let
x = ____________________
y = ____________________
Equations:
_______________________
________________________
EXAMPLE 4: Mariana has 30 nickels and dimes worth $2.60. How many of each coin does she have?
Let
x = ____________________
Equations:
y = ____________________
_______________________
________________________
EXAMPE 5: On December 27th, Jimmy Butler, shooting guard for the Chicago Bulls, scored a total of 33
points. He made a total of 12 shots in the game consisting of all 2 point and 3 point shots. How many of each
type of shot did Butler make?
Let
x = ____________________
y = ____________________
Equations:
_______________________
________________________
6.4 Worksheet 1
Directions:
1.
Read each situation. Define variables, set up a system of equations, and solve your system.
Patrick has 15 coins, some dimes and some quarters. If their value is $2.25, how many of each coin does
he have?
Let
x = ____________________
Equations:
y = ____________________
2.
________________________
Two adult and five student tickets cost $23. One adult and three student tickets cost $13. How much
does each kind of ticket cost?
Let
x = ____________________
Equations:
y = ____________________
3.
________________________
________________________
________________________
The Chicago Bears scored 4 times for a total of 24 points. Their points came from 7-point touchdowns
and 3-point field goals. How many touchdowns and how many field goals did the Bears score in the
game?
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________
4.
Art Club bought some pencils at 25 cents each and paint brushes at 75 cents each. The total number of
pencils plus paint brushes was 55. The total cost was $23.75. How many of each did the club buy?
Let x = ____________________
Equations:
y = ____________________
5.
________________________
Three bananas and one pear cost $ 2.10. Two bananas and three pears cost $3.15. How much does each
item cost?
Let
x = ____________________
Equations:
y = ____________________
6.
________________________
________________________
________________________
Two adult tickets and two children tickets cost $8.50. One adult ticket and two children tickets cost
$6.00. Find the price of each kind of ticket.
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________
6.4 – Word Problems (Day 2) – Mixture Problems
Objective: To write and solve a system of equations modeling real-life problems.
EXAMPLE 1: A dairy owner produces low-fat milk containing 1% fat and whole milk containing 3.5% fat.
How many gallons of each type should be combined to make 100 gallons that is 2% fat?
Let
x = ____________________
Equations:
y = ____________________
_______________________
________________________
EXAMPLE 2: Mixed nuts which cost $8 per pound are made by combining walnuts which cost $6 per pound
with peanuts which cost $9 per pound. Find the number of pounds of walnuts and peanuts required to make 9
pounds of mixed nuts.
Let
x = ____________________
y = ____________________
Equations:
_______________________
________________________
EXAMPLE 3: One antifreeze solution is 20% alcohol. Another antifreeze solution is 12% alcohol. How
many liters of each solution should be combined to make 15 liters of antifreeze solution that is 18% alcohol?
Let
x = ____________________
Equations:
y = ____________________
_______________________
________________________
EXAMPLE 4: Kelly asked you to make 15 gallons of fruit punch that contains 28% fruit juice by mixing
together some amount of Brand A fruit punch and some amount of Brand B fruit punch. Brand A contains 20%
fruit juice and Brand B contains 40% fruit juice. How much of each do you need?
Let
x = ____________________
y = ____________________
Equations:
_______________________
________________________
6.4 Worksheet 2 – Mixture Problems
Directions:
1.
Read each situation. Define variables, set up a system of equations, and solve your system.
A company sells 20 pound bags of mixed nuts that contain 55% peanuts. To make their product they
combine Brand A mixed nuts which contain 70% peanuts and Brand B mixed nuts which contain 20%
peanuts. How many pounds of each brand do they need to use?
Let
x = ____________________
Equations:
y = ____________________
2.
________________________
George asked you to make 12 gallons of fruit punch that contains 24% fruit juice by mixing together
some amount of Brand A fruit punch and some amount of Brand B fruit punch. Brand A contains 14%
fruit juice and Brand B contains 26% fruit juice. How much of each do you need?
Let
x = ____________________
Equations:
y = ____________________
3.
________________________
________________________
________________________
Max wants to make 10 liters of a 41% acid solution by mixing together a 40% acid solution and a 50%
acid solution. How much of each solution does he need to use?
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________
4.
Laura has a 65% saline solution and a 80% saline solution. How many quarts of each solution does she
need to mix together to make 20 quarts of a 71% saline solution?
Let
x = ____________________
Equations:
y = ____________________
5.
________________________
Natalie’s special coffee blend which costs $12 per pound is made by combining Brand X coffee which
costs $24 per pound with Brand Y coffee which costs $10 per pound. How many pounds of each brand
does Natalie use to make 7 pounds of her special coffee blend?
Let
x = ____________________
Equations:
y = ____________________
6.
________________________
________________________
________________________
Tyler wants to make 9 pints of a 25% sugar solution by mixing together a 35% sugar solution and a 20%
sugar solution. How many pints of each solution does he need?
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________
6.4 – Word Problems (Day 3) – Break-Even Problems
Objective: To write and solve a system of equations modeling real-life problems.
EXAMPLE 1: A puzzle expert wrote a new Sudoku puzzle book. His initial costs are $864. Binding and
packaging each book costs $0.80. The book sells for a price of $2. How many copies of the book must be sold
to break even?
Let
x = ____________________
Equations:
y = ____________________
_______________________
________________________
EXAMPLE 2: You earn a fixed salary working as a sales clerk making $11 per hour. You get a weekly bonus
of $100. Your expenses are $65 per week for groceries and $200 per week for rent and utilities. How many
hours do you have to work in order to break even?
Let
x = ____________________
y = ____________________
Equations:
_______________________
________________________
EXAMPLE 3: One satellite radio service charges $10 per month plus an activation fee of $20. A second
service charges $11 per month plus an activation fee of $15.
a.
After how many months is the cost of either service the same?
b.
If you only plan on using satellite radio for 3 months during the summer before cancelling, which plan
would you choose? Why?
Let
x = ____________________
y = ____________________
Equations:
_______________________
________________________
6.4 Worksheet 3 – Break-Even Problems
Directions:
1.
Read each situation. Define variables, set up a system of equations, and solve your system.
Printing a newsletter costs $1.50 per copy plus $450 in printer’s fees. The copies are sold for $3 each.
How many copies of the news letter must be sold to break even?
Let
x = ____________________
Equations:
y = ____________________
2.
________________________
At a local fitness center, members pay a $20 membership fee and $3 for each aerobics class. Non
members pay $5 for each aerobics class. For what number of aerobics classes will the cost for members
and non-members be the same?
Let
x = ____________________
Equations:
y = ____________________
3.
________________________
________________________
________________________
Producing a musical costs $88,000 plus $5900 per performance. Each sold-out performance earns
$7500 in revenue. If every performance sells out, how many performances are needed to break even?
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________
4.
A cell phone provider offers a plan that costs $40 per month plus $0.20 per text message sent or
received. A comparable plan costs $60 per month but offers unlimited text messages.
a.
How many text messages would you have to send or receive in order for the plans to cost the
same amount each month?
b.
If you send or receive an average of 50 text messages each month, which plan would you
choose? Why?
Let
x = ____________________
Equations:
y = ____________________
5.
________________________
There are two different jobs Jordan is considering. The first job will pay her $4200 per month plus an
annual bonus of $4500. The second job pays $3100 per month plus $600 per month toward her rent and
an annual bonus of $500. Which job should she take?
Let x = ____________________
Equations:
y = ____________________
6.
________________________
________________________
________________________
The tennis team wants to purchase T-shirts for its members. Company A charges a $20 set-up fee and
$8 per shirt. Company B charges a $10 set-up fee and $10 per shirt.
a.
How many shirts would have to be purchased for the total cost to be the same at both
companies?
b.
Which company offers a better price for 12 shirts?
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________
6.4 Worksheet 4 – Review
Directions:
1.
Read each situation. Define variables, set up a system of equations, and solve your system.
The yellow pages identify two different local electrical businesses. Business A charges $50 for a service
call, plus an additional $36 per hour for labor. Business B charges $35 for a service call plus an
additional $39 per hour for labor. How many hours would a service call need to be in order for the
companies to charge the same amount?
Let
x = ____________________
Equations:
y = ____________________
2.
________________________
A community sponsored a charity square dance where admission was $3 for adults and $1.50 for
children. If 168 people attended the dance and the money raised was $432, how many adults and how
many children attended the dance?
Let
x = ____________________
Equations:
y = ____________________
3.
________________________
________________________
________________________
A scientist has a container of 2% acid solution and a container of 5% acid solution. How many ounces
of each concentration should be combined to make 25 ounces of 3.2% acid solution?
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________
4.
A carpenter makes and sells rocking chairs. The material for each chair costs $22.50. The chairs sell
for $75 each. If the carpenter spends $420 on advertising, how many chairs must he sell to break even?
Let
x = ____________________
Equations:
y = ____________________
5.
________________________
________________________
You have a piggy bank that has 275 dimes and quarters that total $51.50. How many of each type of
coin do you have in the bank?
Let
x = ____________________
y = ____________________
Equations:
________________________
________________________