2-5 Solving for a Variable
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- Adela Katherine Heath
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1 Warm Up Solve each equation x = m = s = k 6 = 9k + 2
2 Learning Goals 1. Students will use formulas to solve application problems 2-3. Students will solve a formulas and literal equations for a variable
3 A formula is an equation that states a rule for a relationship among quantities. In the formula d = rt, d is isolated. You can "rearrange" a formula to isolate any variable by using inverse operations. This is called solving for a variable.
4 Solving for a Variable Step 1 Locate the variable you are asked to solve for in the equation. Step 2 Identify the operations on this variable and the order in which they are applied. Step 3 Use inverse operations to undo operations and isolate the variable.
5 Example 1: Application The formula C = πd gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol π in your answer.
6 In 2004, Ernst Van Dyk won the wheelchair race of the Boston Marathon with a time of about 1.3 hours. The race was about 26.2 miles. What was his average speed? Use the formula d = rt and round your answer to the nearest tenth.
7 Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour. Construction The formula a = 46c gives the floor area a in square meters that can be wired using c circuits. a. Solve a = 46c for c. b. If a room is 322 square meters, how many circuits are required to wire this room?
8 Construction The formula a = 46c gives the floor area a in square meters that can be wired using c circuits. a. Solve a = 46c for c. b. If a room is 322 square meters, how many circuits are required to wire this room?
9 Example 2A: Solving Formulas for a Variable The formula for the area of a triangle is A = where b is the length of the base, and is the height. Solve for h. bh,
10 Remember! Dividing by a fraction is the same as multiplying by the reciprocal.
11 Example 2B: Solving Formulas for a Variable The formula for a person s typing speed is,where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.
12 Example 2B: Solving Formulas for a Variable The formula for a person s typing speed is,where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for w.
13 The formula for an object s final velocity is f = i gt, where i is the object s initial velocity, g is acceleration due to gravity, and t is time. Solve for i. The formula for the volume of a rectangular prism with length l, width w, and height h is V = lwh. Solve this formula for w. The formula for a Fahrenheit temperature in terms of degrees Celsius is Solve for C. F = 9 5 C + 32
14 The formula for an object s final velocity is f = i gt, where i is the object s initial velocity, g is acceleration due to gravity, and t is time. Solve for i.
15 The formula for the volume of a rectangular prism with length l, width w, and height h is V = lwh. Solve this formula for w.
16 The formula for a Fahrenheit temperature in terms of degrees Celsius is Solve for C. F = 9 5 C + 32
17 A formula is a type of literal equation. A literal equation is an equation with two or more variables. To solve for one of the variables, use inverse operations.
18 Example 3: Solving Literal Equations A. Solve x + y = 15 for x. B. Solve pq = x for q.
19 a. Solve 5 b = 2t for t. b. Solve for V c. Solve m - n = 5 for m. d. Solve m= x for k k e. Solve st + 3t = 6 for s f. m - 4n = 8 for m g. Solve f + 4 g = 6 for f h. Solve b + c = 10 for a. a
20 a. Solve 5 b = 2t for t. b. Solve for V c. Solve m - n = 5 for m. d. Solve m= x for k k
21 e. Solve st + 3t = 6 for s f. m - 4n = 8 for m g. Solve f + 4 g = 6 for f h. Solve b + c = 10 for a. a
22 Lesson Quiz: Part 1 Solve for the indicated variable for h P = R C for C 3. 2x + 7y = 14 for y 4. for m 5. for C
23 Lesson Quiz: Part 2 Euler s formula, V E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. 6. Solve Euler s formula for F. F = 2 V + E 7. How many faces does a polyhedron with 8 vertices and 12 edges have? 6
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