Chapter 1 – Tools of Algebra

1.5 – Rewriting Equations and Formulas

1.5 – Rewriting Equations and Formulas

In this section we will review:Rewriting common formulas and

equations that have more than one variable

1.5 – Rewriting Equations and Formulas

When an equation has more than one variable, you can solve for ANY of the variables.

1.5 – Rewriting Equations and Formulas

Common formulasDistance

• d = rt• d = distance, r = rate, t = time

Simple Interest• I = Prt• I = interest, P = principle, r = rate, t = time

1.5 – Rewriting Equations and Formulas

Common formulasTemperature

• F = 9/5 C + 32• F = degrees Fahrenheit, C = degrees Celsius

1.5 – Rewriting Equations and Formulas Geometry Formulas

Rectangle• Perimeter

• P = 2l + 2w

• Area• A = lw

Triangle• Perimeter

• P = a + b + c

• Area• A = ½ bh

1.5 – Rewriting Equations and Formulas

Geometry FormulasTrapezoid

• Area• A = ½ (b1 + b2)h

Circle• Circumference

• C = πd or C = 2πr

• Area• A = πr2

1.5 – Rewriting Equations and Formulas

Example 1Solve the formula F = ma for a.

1.5 – Rewriting Equations and Formulas

Example 2Solve the formula PE = mgh for h.

1.5 – Rewriting Equations and Formulas Example 3

A conservationist wants to survey a circular lake but cannot measure the diameter of the lake directly. Instead, the conservationist measures the circumference. It is 2 1/3 miles. What is the diameter of the lake, to the nearest ¼ mile?

1.5 – Rewriting Equations and Formulas

Example 4Find the value of y in the equation

3x + 4y = 10 when x = -2 and when x = 6.

1.5 – Rewriting Equations and Formulas

Example 5 A campus bookstore sells T-shirts for $15

each and sweatshirts for $22 each. Write an equation with more than one variable for the bookstore’s revenue R from selling m T-shirts and n sweatshirts.

1.5 – Rewriting Equations and Formulas

Example 6 If the campus bookstore needs to have

$6600 in revenue from sales of these two items. What are some combinations of T-shirts and sweatshirts that will meet this objective?

1.5 – Rewriting Equations and Formulas

HOMEWORK

Worksheet 1.5

#1 – 3, 13 – 25 all