1. Formulas and Equation-Solving
Lesson 19
Introductory Algebra
Formulas and Equation-Solving

2. Warm-Up Area of a Triangle: A = bh Area of a Rectangle: A = lw
Distance: d = rt
Find the area of a rectangle when l = 12 and w = 5.
Find the area of a triangle when b = 6 and h = 7.
Sue drove 3 hours at 52 miles per hour. How far did she drive?

3. Formulas and Equation-Solving
Target:
Solve formulas for a variety of situations.

4. Working with Equations to Solve for a Missing Value
Find the formula that fits the situation given.
Substitute all known values for the variables into the formula.
Determine if any numbers can be multiplied that are on the same side of the equals sign. If so, multiply those numbers.
Solve the equation using inverse operations.
Write out the answer in a complete sentence.

5. Example 1 The area of a triangle is 36 square units. The base is 8
units long. What is the height of the triangle?
Formula: Area = bh
Substitute = (8)h
Multiply = 4h
Solve = h
The height of the triangle is 9 units.

6. Example 2 Kenny deposited $500 in a bank account. After 3 years,
Kenny earned $90 interest. Use the simple interest formula to
determine the interest rate for this account.
Formula: I = prt
Substitute. (90) = (500)r(3)
Multiply (90) = 1500r
Solve = r
Change to a percent (100) = 6%
Kenny earned an interest rate of 6%.

7. Example 3 The volume of a box is 60 cubic inches. The length of the
box is 5 inches and the height of the box is 2 inches. Find
the width of the box.
Formula: Volume = lwh
Substitute = (5)w(2)
Multiply = 10w
Solve = w
The box has a width of 6 inches.

8. Exit Problems
The height of a triangle is 10 inches. The area of the triangle is 30 square inches. What is the length of the triangle’s base?
Jackie has had 50 ‘at bats’ this softball season. She has a batting average of How many hits has she had?
The Parch family drove 8 hours. They traveled a total of 504 miles. What was their rate of speed?

9. Communication Prompt
Describe a situation outside of the math classroom when you would need to use one of the formulas from this lesson.