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

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

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 .

Translate Sentences into Equations

Answer: The equation is .

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

Translate Sentences into Equations

Answer: The equation is .

Answer: The equation is .

Translate each sentence into an equation.

a. A number c multiplied by six is equal to two more than d.

b. Three less than a number a divided by four is seven more than 3 times b.

Translate Sentences into Equations

Writing Equations

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.

Using the four-step problem-solving plan can help you solve any word problem.

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.

Writing Equations

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.

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?

Use the Four-Step Plan

Plan Write an equation to represent the situation. Let h represent the number of hours needed to produce the jellybeans.

1,2500,000 h 10,000,000

Solve

Find h mentally by asking, “What number times 125 equals 1000?”

Answer: It will take 8 hours to produce 10,000,000 jellybeans.

1,250,000 times hours equals 10,000,000.

h = 8

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.

Use the Four-Step Plan

A person at the KeyTronic World Invitational

Answer: It would take 24 minutes.

Type-Off typed 148 words per minute. Howmany minutes would it take to type 3552words?

Use the Four-Step Plan

Let m = the number of minutes needed to type 3552 words

148 times minutes equals 3552

148 m 3552

m 3552 ÷ 148

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.

Answer: The formula is .

Translate the sentence into a formula.

Words Perimeter equals four times the length of the side.

Variables Let P = perimeter and s = length of a side.

The perimeter of a square equals four times the length of the side.

Perimeter equals four times the length of a side.

P 4s

Write a Formula

Answer: The formula is .

Translate the sentence into a formula.

The area of a circle equals the product of and the square of the radius r.

Write a Formula

A = arear = radius

Writing Equations

You can also translate equations into verbal sentences or make up your own verbal problem if you are given an equation.

Translate this equation into a verbal sentence.

Answer: Twelve minus two times x equals negative five.

Twelve minus two times x equals negative five.

12 2x 5

Translate Sentences into Equations

Translate this equation into a verbal sentence.

Answer: a squared plus three times b equals c divided by six.

a squared plus three times b equals c divided by six.

a2 3b

Translate Sentences into Equations

Translate each equation into a verbal sentence.

Answer: Twelve divided by b minus four equals negative one.

Answer: Five times a equals b squared plus one.

1.

2.

Translate Sentences into Equations

4( f + 1.50) – f = 8.25

Write a problem based on the given information.

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?

f = cost of fries f + 1.50 = cost of a burger

Write a Problem

h – 3 = Consuelo’s height in inches

3h(h – 3) = 8262

Write a problem based on the given information.

Answer: Consuelo is 3 inches shorter than Tiana. The product of Consuelo’s height and three times Tiana’s is 8262. How tall is Tiana?

h = Tiana’s height in inches

Write a Problem