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EXAMPLES & SOLUTIONS
Anchor 1
One-variable word problems are real-world problems that contain one unknown value to solve.
Word problems are first created as an algebraic expression.
They are converted into equations to solve a problem.
One-variable word problems have one solution.
ONE-VARIABLE WORD PROBLEM
Examples with explanations of how to solve one-variable word problems
Word Problem
There are 3 apples in a bowl. It takes 10 apples to fill the bowl. What is the additional number of apples needed to flll the bowl?
How do you discover the additional number of apples to fill the bowl?
Gathering Information
The variable is the unknown number of apples needed to fill the bowl. (n).
The constant is the initial number apples in the bowl (3).
The operator is the "+" sign. It means "additional". The unknown 'additional' apples needed (n) must be added to the initial number of apples (3). The expression for the two combined terms (3 + n).
The coefficient is the number of apples increased (multiplied) by one (1) each time a apple is added to the bowl.
The terms are the known number of apples in the bowl (3), the total number of apples (10), and the unknown number (n) of additional apples needed to fill the bowl.
Components
Variable: n
Constant: 3, 10
Operator: '+'
Coefficient: 1
Terms: 3, 10, n
Expression:
3 + n
Write the Equation
Apples: 3
"Additional" means: '+'
Variable: n
Total # of apples: 10
3 + n = 10
SOLVE THE EQUATION
3 + n = 10
3 - 3 + n = 10 - 3
n = 7
Write the Expression
eagle: 2
geese: 4
how many: '+'
variable: triple = x
2 + 4x
Fact: Constant values remain the same, but variables change.
Word Problem
A person went to the video arcade and spent a total of 100 tokens. The person already spent 10 tokens on video games. The rest of the time the person played the Bouncy Ball game, which cost 5 tokens each. How many Bouncy Ball games did the person play?
What is needed to discover how many Bouncy Ball games the person played?
Gathering Information
The variable is the unknown number of Bouncy Ball games the person played (h).
The constant is the number of total tokens spent (100), the initial number of tokens (10), and the cost to play each Bouncy Ball game (5).
The coefficient is the number of tokens, which increases (multiplied) by five (5) each time a game is played.
The first operator is the "*" sign. It means 'each'. The unknown number of games increases by 5 tokens 'each' time a game is played (5h).
The second operator is the "+" sign. It means "added'. The total number of games played, 'each' (5h) must be added to the initial tokens spent (10). (10 + 5h).
The terms are the cost of Bouncy ball games played, each (5h), the initial tokens spent (10), and the total number of tokens spent (100).
Components
Variables: h
Constant: 100, 10
Coefficient: 5
Operators: '*', '+'
Terms: 5h, 10, 100
Expression:
10 + 5h
Write the Equation
Initial tokens spent: 10
"Added" mean: '+'
Cost of each game: 5
"Each" means: '*'
Number of games played: h
Total token cost of all games: 100
SOLVE THE EQUATION
10 + 5h = 100
10 - 10 + h = 100 - 10
0 + h = 90
5h = 90
5 5
n = 18
THE PERSON PLAYED 18 GAMES OF BOUNCY BALL.
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