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Translating Sentences into Equations

August 22, 2011

Translating Sentences into Equations

Objective The student will learn to translate

word sentences into equations.

Translating Sentences into Equations

Applications of algebra frequently require

you to translate word sentences

aboutnumbers into equations. Sometimes

you can translate the words in order. Other

times you may need grouping symbols.

Example

Translate the following sentence:

Twice the sum of a number and four is ten.

2 ∙ 𝑛 + 4 = 10

Example

Translate the following sentence:

When a number is multiplied by four and the result is decreased by six, the result is ten.

4𝑥 −6 = 10

Caution

Be careful when the words “less than” are used. You may not be able to translate the words in order.

Three less than the number x is 12.

𝑥 − 3 = 12

Formulas

Sometimes you will need to use a formula in order to write an equation.

4 4

x

Perimeter = 14

Perimeter = the sum of the lengths of the sides

14 = 4 + 4 + 𝑥

14 = 8 + 𝑥

Formulas

a. Choose a variable to represent the number described by the words inparentheses.

b. Write an equation that represents the given information.

Formulas

The distance traveled in 3 hours of driving was 240 km. (Hourly rate)

a. Let r = the hourly rate

b. Formula: rate time = distance

c. 𝑟 ∙ 3 = 240 , or 3𝑟 = 240

Solution 2

The distance traveled in 3 hours of driving was 240 km. (Hourly rate)

a. Let r = the hourly rate

b. The hourly rate is the number of miles traveled in one hour

c. 𝑟 =240

3

Class work

Oral Exercises

P 20: 1-13

Homework

p 20: 2-16 even, p 21: 17-35 odd, p 22: Mixed Review