Transcript Step 5: Solve the equation (S)

Writing & Solving Equations given real
World Problems
Objectives:
•To solve word problems involving linear equations.
STEPS IN SOLVING WORD PROBLEMS
WITH LINEAR ALGEBRA
VIKINGS KNOW WHY EVERYONE SAILS RIGHT
1. Define the variable that you want to find
with a ‘let’ statement. (V)
2. Identify the key information. (K)
3. Write a word equation. (W)
4. Write a numerical equation. (E)
5. Solve your equation using algebraic
methods and label your solution
appropriately. (S)
6. Check your answer with the conditions
given in the problem and consider whether
your answer is reasonable. (R)
EX 1
1)
A video store charges $8 to rent a video game for
five days. You must be a member to rent from the
store, but the membership fee is free. A video
game club in town charges only $3 to rent a game
for five days, but membership in the club is $50
per year. Which rental plan is more economical?
Step 1: Variable (V) Let x = # of video games rented per year
Step 2: Key information (K)
Video store: $8 to rent game for five days & free membership
Video Game Club: $3 to rent game for five days & $50
membership
EX 1
Step 3: Write word equation (W)
STORE
RENTAL
FEE

NUMBER
RENTED

CLUB
RENTAL
FEE

NUMBER
RENTED

Step 4: Write numerical equation (E)
8 x

3  x  50
CLUB
MEMBERSHIP
FEE
EX 1
Step 5: Solve the equation (S)
If you rent less than 10
video games a year, choose
the Video Store.
8x  3x  50
5x  50
x  10
If you rent 10 video games
a year choose either one.
If you rent more than 10
video games a year, choose
the Video Game Club.
EX 1
Step 6: Conditions/reasonable
Yes, 10 is a reasonable solution since it is a
positive number.
It is also reasonable for someone to rent 10
games per year.
It is reasonable that the Video club would be
more economical if more games are rented
since it has a large membership fee.
EX 2
1)
The bill (parts and labor) for the repair of a car
was $458. The cost of parts was $339. The cost
of labor was $34 per hour. Write and solve an
equation to find the number of hours of labor.
Step 1: Variable (V) Let h = # of hours of labor
Step 2: Key information (K)
Bill was $458
Parts cost $339
Labor cost $34 per hour – 34h
EX 2
Step 3: Write word equation (W)
PARTS + LABOR = BILL
Step 4: Write numerical equation (E)
339  34x  458
EX 2
Step 5: Solve the equation (S)
339  34x  458
34 x  119
x  3.5
The bill includes 3 ½ hours
of labor.
EX 2
Step 6: Conditions/reasonable
Yes, 3.5 is a reasonable solution since it is a
positive number.
3.5 is a reasonable # of hours since it has to be
multiplied by 34 and added to 339 to get the
bill of $458
EX 3
1)
Tyler and Jonathan went to Howies Game Shack to play video
games. Tyler had $50 and played on the xbox that costs $15
per hour. Jonathan arrived at Howies with $35 and played
video games on the computer that costs $10 per hour. After
how many hours will the two boys have the same amount of
money left? How much money will they have left? Can they
continue playing?
Step 1: Variable (V) Let h = # of hours playing video games
Step 2: Key information (K)
Tyler – had $50, cost $15 per hour to play
Jonathan – had $35, cost $10 per hour to play
EX 3
Step 3: Write word equation (W)
Tyler $ start with - $ spent = Jonathan $ start with - $ spent
Step 4: Write numerical equation (E)
50 15h  35 10h
EX 3
Step 5: Solve the equation (S)
50 15h  35 10h
50  35  5h
15  5h
3h
It took 3 hours of playing video games for
the boys to have the same amount of money.
T = 50 – 15h & J = 35 – 10h represents
the amount of money they have left after
h hours.
How much money did they have after 3 hours?
T = 50 – 15h = 50 – 15(3) = $5
So after 3 hours, they will each have $5
left.
Will they continue to play games?
They cannot continue to play the xbox
and computer because Tyler needs $15 to
play for an hour and Jonathan needs $10
to play for the hour. They either will go
home or they can combine their money
and play for an hour on the computer
together.
EX 3
Step 6: Conditions/reasonable
Yes, 3 is a reasonable solution since it is a positive
number.
3 is a reasonable # of hours to play video games.