1. Algebra 3-1 Writing Equations
When writing equations, use variables to represent the unspecified numbers or measures referred to in the sentence or problem.
Then write the verbal expressions as algebraic expressions.
Writing equations
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2. Expressions for equals sign
Algebra 3-1 Writing Equations
Writing Equations
Some verbal expressions that suggest the equals sign are listed below: is
equals
is equal to
is the same as
is as much as
is identical to
Expressions for equals sign
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3. Translate Sentences into Equations
Translate this sentence into an equation.
A number b divided by three is equal to six less than c.
b divided by three is equal to six less than c.
Answer: The equation is .
Example 1-1a

4. Translate Sentences into Equations
Translate this sentence into an equation.
Fifteen more than z times six is y times two minus eleven.
Fifteen more than z times six is y times two minus eleven. 15 z 6 y 2 11
Answer: The equation is .
Example 1-1b

5. Translate Sentences into Equations
Translate each sentence into an equation.
a. A number c multiplied by six is equal to two more than d.
Answer: The equation is .
b. Three less than a number a divided by four is seven more than 3 times b.
Answer: The equation is .
Example 1-1c

6. Algebra 3-1 Writing Equations
Using the four-step problem-solving plan can help you solve any word problem.
Explore the Problem:
To solve a verbal problem, first read the problem carefully and explore what the problem is about.
Identify what information is given.
Identify what you are asked to find.
Plan the Solution:
One strategy you can use to solve a problem is to write an equation.
Choose a variable to represent one of the unspecific numbers in the problem (defining a variable).
Use the variable to write expressions for the other unspecified numbers in the problem.
Estimate the answer if possible.
Explore & Plan
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7. Algebra 3-1 Writing Equations
Solve:
Use your strategy to solve the problem.
If your plan does not work, revise it or make a new plan.
Examine:
Check your answer in the context of the original problem.
Is your answer reasonable and close to your estimate?
Does your answer make sense?
Does it fit the information in the problem?
If not, solve the problem another way.
Solve & Examine
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8. Use the Four-Step Plan
Jellybeans A popular jellybean manufacturer produces 1,250,000 jellybeans per hour. How many hours does it take them to produce 10,000,000 jellybeans?
Explore You know that 1,250,000 jellybeans are produced each hour. You want to know how many hours it will take to produce 10,000,000 jellybeans.
Example 1-2a

9. Use the Four-Step Plan 1,2500,000 h 10,000,000 h = 8
Plan Write an equation to represent the situation. Let h represent the number of hours needed to produce the jellybeans.
1,250, times hours equals 10,000,000.
1,2500,000 h
10,000,000
Solve
Find h mentally by asking, “What number times 125 equals 1000?”
h = 8
Answer: It will take 8 hours to produce 10,000,000 jellybeans.
Example 1-2b

10. Use the Four-Step Plan
Examine If 1,250,000 jellybeans are produced in one hour, then 1,250,000 x 8 or 10,000,000 jellybeans are produced in 8 hours. The answer makes sense.
Example 1-2c

11. Use the Four-Step Plan 148 m 3552 m 3552 ÷ 148
A person at the KeyTronic World Invitational
Type-Off typed 148 words per minute. How
many minutes would it take to type 3552
words?
Let m = the number of minutes needed to type 3552 words
times minutes equals
148 m
3552 m
3552 ÷ 148
Answer: It would take 24 minutes.
Example 1-2d

12. Algebra 3-1 Writing Equations
A formula is an equation that states a rule for the relationship between certain quantities.
Sometimes you can develop a formula by making a model.
Formula
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13. Write a Formula P 4s Translate the sentence into a formula.
The perimeter of a square equals four times the length of the side.
Words Perimeter equals four times the length of the side.
Variables Let P = perimeter and s = length of a side.
Perimeter equals four times the length of a side. P 4s
Answer: The formula is .
Example 1-3a

14. A = area r = radius Write a Formula
Translate the sentence into a formula.
The area of a circle equals the product of  and the square of the radius r.
Answer: The formula is .
A = area
r = radius
Example 1-3b

15. Translate equations into verbal
Algebra 3-1 Writing Equations
Writing Equations
You can also translate equations into verbal sentences or make up your own verbal problem if you are given an equation.
Translate equations into verbal
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16. Translate Sentences into Equations
Translate this equation into a verbal sentence. x
Twelve minus two times x equals negative five.
Answer: Twelve minus two times x equals negative five.
Example 1-4a

17. Translate Sentences into Equations
Translate this equation into a verbal sentence.
a b
a squared plus three times b equals c divided by six.
Answer: a squared plus three times b equals c divided by six.
Example 1-4b

18. Translate Sentences into Equations
Translate each equation into a verbal sentence. 1.
Answer: Twelve divided by b minus four equals negative one. 2.
Answer: Five times a equals b squared plus one.
Example 1-4c

19. Write a Problem f = cost of fries f + 1.50 = cost of a burger
Write a problem based on the given information.
f = cost of fries
f = cost of a burger
4( f ) – f = 8.25
Answer: The cost of a burger is $1.50 more than the cost of fries. Four times the cost of a burger minus the cost of fries equals $8.25. How much do fries cost?
Example 1-5a

20. h = Tiana’s height in inches
Write a Problem
Write a problem based on the given information.
h = Tiana’s height in inches
h – 3 = Consuelo’s height in inches
3h(h – 3) = 8262
Answer: Consuelo is 3 inches shorter than Tiana. The product of Consuelo’s height and three times Tiana’s is How tall is Tiana?
Example 1-5b