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1.4 Rewrite Formulas and Equations

Formula

An equation that relates two or more quantities, usually represented by variables

Solve for a variable

To rewrite an equation as an equivalent equation in which the variable is on one side and does not appear on the other side

Example 1

Rewrite a formula with two variables

Solve the formula C = 2pr for r. Then find the radius of a circle with a circumference of 26 meters.

Step 1	Solve the formula for r.
	C = 2pr	Write original circumference formula.
	_{____}^{= r}
	_{____}^{= r}	Divide each side by _2p_.
Step 2	Substitute the given value into the rewritten formula.
	^r⁼____ ⁼_____ ^» ^__4__	Substitute __26__ for C and simplify.
The radius of the circle is about __4__ meters.

Example 2

Rewrite a formula with three variables

Solve the formula A = l · w for l. Then find the length of a rectangle with a width of 11 feet and an area of 187 square feet.

Solution

Step 1	Solve the formula for l.
	A = l · w	Write area formula.
	_{______}^{= l}	Divide both sides by __w__.

Step 2	Substitute the given value into the rewritten formula.
	^l⁼_{____}		Substitute__187__ for A and __11__ for w
	= __17__		Simplify.
The length of the rectangle is __17__ feet.

Complete the following exercises.

1. Solve the formula P = 2l + 2w for w. Then find the width of a rectangle with a length of 9 meters and a perimeter of 32 meters.

7 meters

2. Solve the distance formula d = rt for t. Then find the time it takes to travel the distance of 135 miles at a rate of 30 miles per hour.

4.5 hours

Example 3

Rewrite a linear equation

Solve 5x - 4y = 9 for y. Find y when x = -3.