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Activity 1 - 11
Comparing Energy Costs
or
How Long Until Renewable Energy
is Affordable
5-Minute Check on Activity 1-10
1. Using your calculator solve the following:
y=6
y = ex
x = 1.792, y = 6
Using algebra solve the following:
2. y = 3x – 5 where y = 10
x=5
3. y = 30 – 2x where y = 24
x=3
4. y = (3/4)x – 21 where y = -9
5. y = 15 – 2x where y = -3
Click the mouse button or press the Space Bar to display the answers.
x = 40
x=6
Objectives
• Develop mathematical models to solve problems
• Write and solve equations of the form ax +b = cx + d
• Use the distributive property to solve equations
involving grouping symbols
• Solve formulas for a specified variable
Vocabulary
• none new
Activity
An architect is hired to design a house. She obtains
the following information regarding the installation and
operating costs of two types of heating systems: solar
and electric.
Heating System
Installation Cost
Operating Cost (per yr)
Solar
$25,600
$200
Electric
$5,500
$1600
Solar
Heating System
Installation Cost
Operating Cost (per yr)
Solar
$25,600
$200
Electric
$5,500
$1600
a) Determine the 5 year total cost of the solar system
Cost = 25,600 + 5(200) = 26,600
b) Write a statement for the total cost in terms of the number of
years of use
Cost is installation cost plus yearly operating cost
c) Letting x = years of use and c = total cost, write an equation
from statement in b)
Cost = 25,600 + 200yrs
d) Fill out the table:
Years of use, x
Total Cost, c
5
10
15
26,600
27,600
28,600
20
29,600
Electric
Heating System
Installation Cost
Operating Cost (per yr)
Solar
$25,600
$200
Electric
$5,500
$1600
a) Determine the 5 year total cost of the electric system
Cost = 5,500 + 5(1600) = 13,500
b) Write a statement for the total cost in terms of the number of
years of use
Cost is installation cost plus yearly operating cost
c) Letting x = years of use and c = total cost, write an equation
from statement in b)
Cost = 5,500 + 1600yrs
d) Fill out the table:
Years of use, x
Total Cost, c
5
10
15
13,500
21,500
29,500
20
37,500
Solar vs Electric
Heating System
Installation Cost
Operating Cost (per yr)
Solar
$25,600
$200
Electric
$5,500
$1600
a) Compare the table values from the previous slides
Years of use, x
5
10
15
20
Solar
26,600
27,600
28,600
29,600
Electric
13,500
21,500
29,500
37,500
b) Estimate in what year will the Electric’s cost exceed the Solar’s
looks like about year 14 sometime
c) Write an equation that can be solved algebraically to determine
what year the two costs would be equal
25600 + 200x = 5500 + 1600x
Accord vs Passat
Car
MSRP
Annual Depreciation
Accord LX
$20,925
$1730
Passat GLS
$24,995
$2420
a) Fill out the table below reflecting each car’s value
Years Owned
1
2
3
4
Accord
19,195
17,465
15,735
14,005
Passat
22,575
20,155
17,735
15,315
b) Will the value of the Passat ever be lower than the Accord
Not in this time frame, but soon
c) Write an equation to figure out when their values would be equal
20925 – 1730x = 24995 – 2420x
d) Solve the equation
690x = 4070
x = 5.89
Formulas
Solve each of the following formulas for the
specified variable
A = lw
A/l = w
a) A = lw for w
b) P = 2l + 2w for l
P = 2l + 2w
c) V = πr²h for h
V = r²h
d) V(P + a) = k for P
(P – 2w)/2 = l
V/(r²)= h
V(P + a) = k
V = k/(P + a)
Equations
Solve each of the following equations for x
a) 2x + 9 = 5x – 12
9 = 3x – 12
b) 21 – x = -3 – 5x
21 + 4x = -3
c) 2(x – 3) = -8
2x – 6 = -8
21 = 3x
4x = -24
2x = -2
7=x
x = -6
x = -1
d) 2(x – 4) + 6 = 4x – 6
2x – 8 + 6 = 4x – 6
-2 = 2x – 6
2x – 2 = 4x – 6
4 = 2x
2=x
Summary and Homework
• Summary
– General strategy for solving equations for a variable
•
•
•
•
•
Remove parentheses (distributive property)
Combine like terms on the same side of equation
Get all variables to one side and the “just” numbers to other
Divide through by the variable’s coefficient
Check the result in the original equation
– To solve a formula for a variable, isolate that variable
on one side of the equation and all other terms on
the other side
• Homework
– pg 100-6; 4-11, 20-25