Word Problems
There are special roller coasters in an arcade, which cost an extra fee, the Howling Hurricane and the Crazy Catastrophe. One day, 12 people rode the Howling Hurricane and 18 people rode the Crazy Catastrophe, and the museum made 450 dollars off of just those two rides' extra fees. On the second day, 24 people rode the Howling Hurricane and 12 people rode the Crazy Catastrophe, and the museum made 720 dollars off of just those two exhibits' extra fees. How much is fee for the Howling Hurricane? How much is fee for the Crazy Catastrophe?
Howling Hurricane - $15
Crazy Catastrophe - $20
x+y+z=40
x=2y
z=5y
x=10
y=5
z=25
When is it best to use substitution?
You should use substitution when you have a variable with a coefficient of 1.
x + y = 12
x = 1/3y
(3,9)
Carl and Joe sell clothing. They earn a commission for each shirt and each pair of shoes they sell. If Carl sells 3 shirts and one pair of shoes, and earns $47, and Joe earns $107 for selling 7 suits and 2 pairs of shoes, how much do Joe and Carl earn for each pair of shoes they sell? What about shirts?
$13 for each shirt
$8 for each pair of shoes
x-y=x+y
Solve for y
y=0
What is the proper format for writing a system of equations?
Will be written on the board
1/2x + 2y = 12
x = 3y - 11
Write your solution as an ordered pair
(4,5)
Find two integers whose sum is 92, if the first is 4 more than 7 times the second.
81, 11
2x-y=6
x+y=-3
Write your solution as an ordered pair.
(1,-4)
When solving a system of equations with substitution, what is the first step?
The first step it to set the equation up so that one of your variables, without a coefficient, is given a value in terms of the other equation
ex. y+x=2
y = 2-x
5x - y = 8
y = 2/3x + 5
Write your solution as an ordered pair.
(3,7)
The sum of three integers is 61. The second integer is 5 times the first, while the third is two less than the first. Find the integers
9, 45, 7
X-Y=X+Y
X^X=1
No solution
What are the two different methods of substitution?
Making both of the equations in terms of one variable, and solve the equations by making them equal to each other.
Give one variable a value, and substitute that value for the variable.
y = 3/4x - 2/8
1 = y + 1/3 - 2/3x
Write your solution as an ordered pair.
11,8
A museum has two special exhibits, the Space Shuttle and the World War two submarine, that cost an extra admission fee. One day, 13 people visited the Space Shuttle exhibit and 17 people visited the World war two submarine, and the museum made 514 dollars off of just those two exhibits' extra fees. On the second day, 18 people visited the Space Shuttle exhibit and 12 people visited the World War II submarine, and the museum made 504 dollars off of just those two exhibits' extra fees. How much is admission fee for the Space Shuttle exhibit? How much is admission fee for the World War II submarine?
Space Shuttle Exhibit - $16
World War II Submarine Exhibit - $18
x - 2y - z = -4
5x - 4y + z = 4
2x + 3y + z = 8
x = 1
y = 1
z = 3
How does substitution work?
Substitution works because the equation is the same; the values are not being changed. Only the way they are written are changed.
x = 5/6y - 1
2/7 = 2x + y
(-2/7, 6/7)