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Solving Variables in Mathematical Formulas: Examples and Solutions, Assignments of Algebra

State College of Florida, Manatee-Sarasota (SCF)Algebra

Examples and solutions for solving variables in mathematical formulas, including the area and perimeter of rectangles and triangles, temperature conversions, and distance calculations. It covers formulas for finding specific variables such as width, height, and rate, and includes exercises for practice.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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MAT 1033 Solving Formulas for Specified Variables Section 2.3
Notice that the formula for the area of a rectangle
LWA
is solved for A. To solve for W, we want to
get W alone on one side of the equation. To do this, divide both sides of the equation by L.
W
L
A
L
LW
L
A
LWA
Solve for the indicated variable:
1.
ghW
for g2.
lwhV
for h
3.
hrV
2
for
h
4.
bhV 3
1
for b
The formula for the perimeter of a triangle
cbaP
is solved for P. To solve for a, we want to get a
alone on one side of the equation. To do this, subtract b and c from both sides of the equation.
Solve for the indicated variable:
5.
52 yx
for y6.
423 yx
for y
Working with Formulas
pf3

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MAT 1033 Solving Formulas for Specified Variables Section 2. Notice that the formula for the area of a rectangle A^ ^ LW is solved for A. To solve for W , we want to get W alone on one side of the equation. To do this, divide both sides of the equation by L. W L A L LW L A A LW    Solve for the indicated variable:

  1. W^ ^ gh for g 2. V^  lwh^ for h
  2. V   r^2 h for h^ 4. V^ bh 3 1  (^) for b The formula for the perimeter of a triangle P^  a^  bc is solved for P. To solve for a , we want to get a alone on one side of the equation. To do this, subtract b and c from both sides of the equation. P b c a P b c a b c b c P a b c              Solve for the indicated variable:
  3. ^2 x^  y ^5 for y 6. 3 x^ ^2 y ^4 for y Working with Formulas
  1. A formula relating degrees Fahrenheit with degrees Celsius is 32 5 9 FC . a) If the temperature in Nome, Alaska is –15ºC, what is the temperature in degrees Fahrenheit? b) Solve the equation for C. c) If the temperature in Bradenton, Florida is 95ºF, what is the temperature in degrees Celsius?
  2. Use the formula d^  rt^ “distance = rate·time” to determine the following: a) If you have been driving north on I-75 for 3 hours at 75 miles per hour how far have you driven? b) Solve the equation for r. c) It took you and your family 5.5 hours round-trip to drive from your house to the family beach house 154 miles away. Find the average speed of the trip.
  3. The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat and protein. The calorie count C for a serving of food can be computed using the formula