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4.4 Solving for a Variable in a Linear Equation.notebook
March 26, 2015
2015 03 26
Reminder: Tonight is PT night!
3:30 to 6:30.
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4.4 Solving for a Variable in a Linear Equation.notebook
2015 03 26
March 26, 2015
4.4 Solving for a Variable in a Linear Relation
Problem:
Ralph and Bill work part time repairing bikes. They are paid $2 to install a tire and $5 to install gears. Their boss will pay a maximum of $100 per week.
Which combinations of tire and gear installations will earn the boys exactly $100?
Solution:
Develop an equation to model the relation!
2t + 5g = 100
Method 1: Table of Values ­ choosing a value for one variable and solving for the other
g
t
0
5
10
15
20
25
30
2(0) + 5g = 100 ⇒g = 20
2(5) + 5g = 100 ⇒g = 18
2(10) + 5g = 100 ⇒g = 16
2(15) + 5g = 100 ⇒g = 14 2(20) + 5g = 100 ⇒g = 12
2(25) + 5g = 100 ⇒g = 10 2(30) + 5g = 100 ⇒g = 8
Method 2: Solve for a variable in terms of another. the process of using inverse operations to express one variable in terms of the other variable﴾s﴿
Isolate g !
2t + 5g = 100
2t + 5g = 100
5g = 100 ­ 2t
g = 100 ­ 2t
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4.4 Solving for a Variable in a Linear Equation.notebook
March 26, 2015
Example 2:
move the 'x' term over to the right hand side of the equation by subtracting !
multiply both sides by '5' to cancel out the fraction 1/5
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4.4 Solving for a Variable in a Linear Equation.notebook
March 26, 2015
2. Henri sharpens skates at a local arena. He charges $3.00 to sharpen a pair of figure skates and $2.50 for a pair of hockey skates. Last Saturday he earned a total of $240.
a) To model this situation, John wrote: $3(number of pairs of figure skates) + $2.5(number of pairs of hockey skates) = $240. Write the relation using variables.
3f + 2.5h = 240
b) Write the equation that expresses the number of hockey skates sharpened in terms of the number of figure skates.
c) Write the equation that expresses the number of figure skates sharpened in terms of the number of hockey skates.
Assigned Work:
pp. 236 ­ 237 #4, 7ace, 6, 9, 10, 13c 4