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EXAMPLES & SOLUTIONS
Anchor 1
They are variables that form a relationship, in which a variable-value depends on value of another variable to solve a equation, function or problem.
One variable is the dependent & the other is the independent.
The independent variable causes a change in the dependent variable.
The independent variable can stand alone.
A independent variable is not effected by the dependent variable.
DEPENDENT AND INDEPENDENT VARIABLE WORD PROBLEM
Understanding dependent and independent variables in word problems
Fact: Dependent variables depend on the variables of the independent variable.
A soccer team scores points during a game. After each shot the team scores 2 points. What is the score after 6 shots?
UNKNOWN
What do you need to discover?
The score after 6 shots.
KNOWN
What is known about the shots?
Each shot is 2 points.
The team score (y = ?) depends on the number of shots (x = 6)
2 = points per shot = the score changes by 2 each time the team scores
x = number of shots = independent = 6 points
y = score = dependent = total score
EXPRESSION: y = 2x
SOLUTION: y = 2 (6)
y = 12
A person score is 12 after 6 shots.
ANOTHER DEPENDENT & INDEPENDENT VARIABLES WORD PROBLEM
A person went to the video arcade. The person played Bouncy Ball that cost 5 tokens each game. If the person played 18 Bouncy Ball games, how much will the person spend in all?
UNKNOWN
What do you need to discover?
The amount spent after 18 games.
KNOWN
What is known about the game?
Each game cost 5 tokens.
The cost of the total games (m = ?) played depend on the number of games played (n= 18)
5 = cost of each game = the cost increases by 5 tokens after each a game is played.
n = number of games played = independent = 18 games
m = spent = dependent = total cost
EXPRESSION: 5n = m
SOLUTION: 5(18) = m
m = 90
The total cost after 18 games is 90 tokens.
Write the Expression
eagle: 2
geese: 4
how many: '+'
variable: triple = x
2 + 4x
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