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EXAMPLES & SOLUTIONS
Solving Equations: Two-Variable Word Problem
Anchor 1
A two-variable equation has more than one variable that needs to be solved.
They solve unknown variables.
These variables are presented as letters.
TWO-VARIABLE WORD PROBLEM
Examples with explanations of how to solve two-variable word problems
A soccer team scores points during a game. After each shot the team scores 2 point. What is the score when the team makes 6 shots?
How do we determine the score after 6 shots?
Gathering Information
The variables are the unknown number of shots (n), and the unknown score (m).
There isn't a constant.
The operator is the "*" sign. It means "each". The unknown number of shots (n) is multiplied by the number of points (2) 'each' time a shot is made. (2n).
The coefficient is the points that are increased by two (2)' each' time shot is made.
The terms are the unknown number of shots (n), the unknown score (m) and the number of points per shot (2).
Components
Variable: m & n
Constant: none
Operator: '*'
Coefficient: 2
Terms: 2, n, m
Expression:
2* n
Write the Equation
Points each: 2
Number of shots: n
"Each" means: '*'
Total score: m
2n = m
SOLVE THE EQUATION
6
n
2 * n
m
1
2
3
3
4
0
2
4
6
8
2 * 0
2 * 1
2 * 2
2 * 3
2* 4
10
2 * 5
5
2 * 6
?
IF A PERSON MAKES 6 SHOTS, WHAT IS THE SCORE?
if n = 6, then,
2 * n = m
2 * 6 = m
12 = m
AFTER 6 SHOTS (n) THE SOCCER TEAM SCORES 12 POINTS (m).
Fact: One variable depends on the other variable
Word Problem
A person went to the video arcade. The person already spent 10 tokens on one video game. The rest of the time the person played Bouncy Ball that cost 5 tokens each game. If the person played 18 Bouncy Ball games, how much did the person spend on tokens?
How do we determine the number of tokens spent when a person plays 18 (h) Bouncy Ball games?
Discover how to get the number of shots to get the score
Gathering Information
The variables are the unknown total number of tokens spent by the person (x). and the unknown variable when a person played (h) games.
The constant is the number of initial tokens (10), and the cost for each Bouncy Ball game (5).
The first operator is the "*" sign. It means 'each'. It means to multiply 'each' unknown number of games played (h) by the cost per token (5).
The second operator is the "+" sign. It means 'how much', It mean to add the cost of the Bouncy Ball games (5h) to the initial number of tokens (10) spent to discover how much the total games cost.
The coefficient is the token cost per game (5).
The terms are the cost of the Bouncy Ball games (5h), the initial number of tokens (10) and how much the total games cost (x).
Components
Variables: h, x
Terms: 10, 5, h, x
Coefficient: 5
Constant: 10
Operator: '+'
Expression:
10 + 5h
Write the Equation
Initial tokens: 10
"How much" mean: '+'
Cost of each game: 5
"Each" means: '*'
Number of games: h
Total tokens (cost): x
10 + 5h = x
SOLVE THE EQUATION
.
.
.
.
.
.
.
.
.
h
10 + 5h
x
1
2
3
4
5
15
20
25
30
35
10 + 5(1)
10 + 5(2)
10 + 5(3)
10 + 5(4)
10 + 5(5)
6
40
10 + 5(6)
18
?
10 + 5(18)
IF A PERSON PLAYS 18 GAMES, WHAT IS THE COST?
if h = 18, then,
10 + 5(18) = x
10 + 90 = x
x = 100
AFTER 18 BOUNCY BALL GAMES (h) , THE TOTAL AMOUNT SPENT IS 100 TOKENS (x) .
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