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2-5

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2-5

Solving for a Variable

Warm Up

Lesson Presentation

Lesson Quiz

Holt Algebra 1

1) Find two consecutive integers whose sum is 47.

- Define your Variables:
Let x = the first integer

Let = the second integer

x + 1

b. Write your equation and solve:

x + (x + 1) = 47

2x + 1 = 47

2x = 46 x = 23

c. Lastly, answer the question: 23, 24

1) Find two consecutive even integers whose sum is 110.

- Define your Variables:
Let x = the first integer

Let = the second integer

x + 2

b. Write your equation and solve:

x + (x + 2) = 110

2x + 2 = 110

2x = 108 x = 54

c. Lastly, answer the question: 54, 56

1) The larger of two numbers is 1 less than three times the smaller. The difference between the two numbers is 9. Find the numbers.

- Define your Variables:
Let x = the smaller number

Let = the larger number

3x - 1

b. Write your equation and solve:

(3x - 1) - x = 9

2x - 1 = 9

2x = 10 x = 5

c. Lastly, answer the question: 5, 14

Warm Up

1. Stan’s, Mark’s and Wayne’s ages are consecutive whole numbers. Stan is the youngest, and Wayne is the oldest. The sum of their ages is 111. Find their ages.

2. The sum of two consecutive even whole numbers is 206. What are the two numbers? (Hint: Let n represent the first number. What expression can you use to represent the second number?)

3. The height of an ostrich is 20 inches more than 4 times the height of a kiwi. The ostrich is 108 inches tall. Write and solve an equation to find the height of a kiwi.

36, 37, 38

102, 104

4k + 20 = 108

22 in.

OR

kiwi

kiwi

(Warm Up) – Hurricane QUIZ On Blank Notebook Paper

Solve each equation.

- m + 13 = 58
- .
- 2y + 29 – 8y = 5
- 4(3x + 1) – 7x = 6 + 5x – 2
5) Find two consecutive integers whose sum is 47.

45

40

4

All real numbers

23, 24

Warm Up

Solve each equation.

1. 5 + x = –2

2. 8m = 43

3.

4. 0.3s + 0.6 = 1.5

5. 10k – 6 = 9k + 2

–7

19

3

8

Objectives

Solve a formula for a given variable.

Solve an equation in two or more variables for one of the variables.

Vocabulary

formula

literal equation

- If it is 85ºF outside, what is that temperature in degrees Celsius?

- Formula:

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.

Example 1: Application

The formula C = d 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 in your answer.

Locate d in the equation.

Since d is multiplied by , divide both sides by to undo the multiplication.

Now use this formula and the information given in the problem.

The bowl's diameter is inches.

Example 1: Application Continued

The formula C = d 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 in your answer.

Now use this formula and the information given in the problem.

Check It Out! Example 1

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.

d = rt

Locate t in the equation.

Since t is multiplied by r, divide both sides by r to undo the multiplication.

Now use this formula and the information given in the problem.

Check It Out! Example 1

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.

Van Dyk’s time was about 1.46 hours.

A = bh

Since bh is multiplied by , divide both sides by to undo the multiplication.

Example 2A: Solving Formulas for a Variable

The formula for the area of a triangle is A = bh,

where b is the length of the base, and is the height. Solve for h.

Locate h in the equation.

2A = bh

Since h is multiplied by b, divide both sides by b to undo the multiplication.

Remember!

Dividing by a fraction is the same as multiplying by the reciprocal.

ms = w – 10e

–w –w

ms – w = –10e

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.

Locate e in the equation.

Since w–10e is divided by m, multiply both sides by m to undo the division.

Since w is added to –10e, subtract w from both sides to undo the addition.

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.

Since e is multiplied by –10, divide both sides by –10 to undo the multiplication.

Remember!

Dividing by a fraction is the same as multiplying by the reciprocal.

f = i – gt

+ gt +gt

Check It Out! Example 2

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.

f = i – gt

Locate i in the equation.

Since gt is subtracted from i, add gt to both sides to undo the subtraction.

f + gt = i

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.

–y –y

x = –y + 15

Example 3: Solving Literal Equations

A. Solve x + y = 15 for x.

x + y = 15

Locate x in the equation.

Since y is added to x, subtract y from both sides to undo the addition.

B. Solve pq = x for q.

pq = x

Locate q in the equation.

Since q is multiplied by p, divide both sides by p to undo the multiplication.

Check It Out! Example 3a

Solve 5 – b = 2t for t.

5 – b = 2t

Locate t in the equation.

Since t is multiplied by 2, divide both sides by 2 to undo the multiplication.

Solve for V

Check It Out! Example 3b

Locate V in the equation.

Since m is divided by V, multiply both sides by V to undo the division.

VD = m

Since V is multiplied by D, divide both sides by D to undo the multiplication.

- If it is 85ºF outside, what is that temperature in degrees Celsius?

- Formula:

Lesson Quiz: Part 1

Solve for the indicated variable.

1.

2.

3. 2x + 7y = 14 for y

4.

for h

P = R – C for C

C = R – P

for m

m = x(k – 6)

5.

for C

C = Rt + S

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