2-8 Literal Equations and Dimensional Analysis 2-8 Literal Equations and
Dimensional Analysis
A Review
Essential Question: Why is it import to be able to
express equations in several ways?
Activities for the day:
Warm-up
Review Percent of Change
Powerpoint for Literal equations and dimensional
analysis
Discuss test
Classwork/homework
Find three consecutive integers whose sum is 48.
Find two consecutive even integers who sum is 66.
Review
Name:_______________
Find three consecutive even integers such that the
sum of the smallest and largest is 36.
The width of a rectangle is 12 cm less than the length.
The perimeter is 156 cm. Find the width and the
length.
The perimeter of a triangle is 76 cm. Side
a of the triangle is twice as long as side b.
Side c is 1 cm longer than side a. Find the
length of each side.
In an isosceles, that is a triangle with two sides of
equal length. The third side is 30 m shorter than
twice the length of each congruent side. The
perimeter is 570m. Find the length of each side.
A Review
State whether the percent of change is a percent of
increase or a percent of decrease. Then find the
percent of change. Round to the nearest whole
number.
Original :84
New: 96
State whether the percent of change is a percent of
increase or a percent of decrease. Then find the
percent of change. Round to the nearest whole
number.
Original :47
New:18
What is the discounted price of a tent with a price of
\$89 and a discount of 15%?
What is the final price of a pair of hiking boots with a
price of \$78, a discount of 10%, and a tax of 6%?
A Review
On July 1, a stock sold for \$46 per share, and on
August 1, it sold for \$48.30 per share. What was the
percent of change in the price of the stock?
Olivia’s cell phone bill last month was \$125. the
month her bill is \$85. what is the percent of change?
Objective of today’s lesson:
• Solve equation for given variables
• Use formulas to solve real-world
problems
New vocabulary:
• Literal equation
• Dimensional analysis
• Unit analysis
Solve for a specific variable
5b + 12c = 9
Solve for b
7x – 2z = 4 – xy
Solve for x
2x – 17y = 13 Solve for y
• Note division by 0 is undefined,
therefore y ≠___________
More examples
12a + 3c = 2ab + 6
Solve for a
A car’s ful economy E (miles per
𝑚
gallon is given by the formula E =
𝑔
Where m is the number of miles driven and g is
the number of gallons of fuel used. Solve the
formula for m.
If Quananh’s car has an average fuel
consumption of 30 miles per gallon and she
used 9.5 gallons, how far did she drive?
Real-World Problems
A car’s fuel economy E (miles per gallon) is
𝑚
given by the formula E = , where m is the
𝑔
number of miles driven and g is the number of
gallons of fuel used. Solve the formula for g.
The average weight of the chimpanzees at
a zoo is 52 kilograms. If 1 gram is about
.0353 ounce, use dimensional analysis to
find the average weight of a chimpanzee
in poiunds. (Hint: 1 lb = 16 oz)
If Quanan drove 1477 miles and her pickup has an
average fuel consumption of 119 miles per gallon,
about how many gallons of fuel did she use?
Janet is walking 20 laps of a track in a relay to raise
money for cancer research. If each lap is 350 meters,
how many miles will Janet walk?
(Hint: 1 meter is about 1.094 yards and 1 mile + 1760
yards)