1. CLOSE Please YOUR LAPTOPS, and get out your note-taking materials.
and turn off and put away your cell phones,
and get out your note-taking materials.

2. Section 2.5 Using Formulas

3. Formula
A formula is an equation that states a known relationship among multiple quantities (has more than one variable in it).

4. Examples of Formulas A = lw (Area of a rectangle = length · width)
NOTE: You DO NOT have to memorize these formulas.
You DO have to know how to use them.
Examples of Formulas
A = lw (Area of a rectangle = length · width)
I = PRT (Simple Interest = Principal · Rate · Time)
P = a + b + c (Perimeter of a triangle = side a + side b + side c)
d = rt (distance = rate · time)
V = lwh (Volume of a rectangular solid = length · width · height)
C = 2r (Circumference of a circle = 2 ·  · radius)

5. Example: 12 12

6. Example: Relevant formula:
A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 30 feet more than the length of the shortest side. Find the dimensions if the perimeter is 102 feet.
Relevant formula:
P = a + b + c (Perimeter of a triangle = side a + side b + side c)
Understand and Translate:
Read and reread the problem.
If we let x = the length of the shortest side,
then 2x = the length of the second side,
and x + 30 = the length of the third side.
Perimeter = sum of all the sides = x + 2 x + x + 30
So x + 2 x + x + 30 = 102
x x
x + 30

7. Example (cont.) Solve 102 = x + 2x + x + 30
102 = 4x (simplify right side)
102 – 30 = 4x + 30 – 30 (subtract 30 from both sides)
72 = 4x (simplify both sides)
(divide both sides by 4)
18 = x (simplify both sides)

8. Example (cont.) Interpret
Check: If the shortest side of the triangle is 18 feet, then the second side is 2(18) = 36 feet, and the third side is = 48 feet.
This gives a perimeter of P = = 102 feet, the correct perimeter.
State: The three sides of the triangle have a length of 18 feet, 36 feet, and 48 feet.

9. It is often necessary to rewrite a formula so that it is solved for one of the variables.
This is accomplished by isolating the designated variable on one side of the equal sign.

10. Steps for Solving Formulas:
Multiply to clear fractions.
Use distributive property to remove grouping symbols (parentheses and brackets).
Combine like terms to simplify each side.
Get all terms containing specified variable on the same side, all other terms on opposite side.
Isolate the specified variable (using the distributive property in reverse if more than one term).
Divide both sides by the quantity that’s now in front of the variable you’re solving for. (If you had more than one term containing the variable you’re solving for, his will be an expression in parentheses.)

11. Example 1: Solve the formula for n:
(divide both sides by mr)
(simplify right side)

12. Example 2: Solve the formula for T
(Subtract P from both sides)
(Simplify right side)
(Divide both sides by PR)
(Simplify right side)

13. Example 3: Solve the formula for P
(Isolate P by factoring out P from both terms on the right side)
(Divide both sides by
(1 + RT)
(Simplify the right side)

14. Example 4: Solve for v T = 3vs – 4ws + 5vw T + 4ws = 3vs + 5vw
Get rid of terms on right that don’t have a v,
i.e. add 4ws to both sides:
T + 4ws = 3vs + 5vw
Isolate the v on the right by factoring it out of both terms:
T + 4ws = v(3s + 5w)
Divide both sides by the part in parentheses:
T + 4ws = v(3s + 5w)
(3s + 5w) (3s + 5w)
Simplify by canceling the common part on the right:
T + 4ws = v DONE!
3s + 5w

15. Example from today’s homework:
Solve 𝑇=𝐶 5+𝐴𝐵 for 𝐴.
Answer: T – 5C or T
BC BC B
(These two versions of the answer are equivalent and either one is accepted. Which form of the answer you get depends on whether you divide both sides by C as your first step [gives first answer] vs. if you distribute the C on the right side first [gives second answer].)

16. HW NOTE: Dealing with negatives in the denominator:
EXAMPLE: Solve 6x – 7y = 15 for y
1. Subtract 6x from both sides:
-7y = 15 – 6x
2. Divide both sides by -7:
y = 15 – 6x -7
3. This is the answer, but not in simplified form. We must multiply the top and bottom by -1 to make the denominator positive:
y = -1(15 – 6x) = x = 6x - 15
-1(-7)

17. Visit the MathTLC for homework help!
The assignment on this material (HW 2.5)
Is due at the start of the next class session.
Visit the MathTLC
for homework help!

18. and begin working on the homework assignment.
You may now OPEN
your LAPTOPS
and begin working on the homework assignment.
We expect all students to stay in the classroom to work on your homework till the end of the 55-minute class period. If you have already finished the homework assignment for today’s section, you should work ahead on the next one or work on the next practice quiz/test.