the comparison (equals) and tells us what to put on the left of the equal sign, and what to put on the right of the equal sign.

x + 12

The sum of a number and 12 is 78.

x + 5

**Ch. 1.4 - 1.6: Translating Words into Mathematical Symbols and Statements**

**Translating Words into Symbols (Ch. 1.4)**

Translating Sentences into Equations (Ch. 1.5)

How to translate word sentences into mathematical equations.

Translating Word Problems into Mathematical Problems (Ch. 1.6)

The goal in these problems is to arrive at a single equation with a single variable.

Now that we know how to "decode" the math-words into math equations, we can begin to translate whole word problems into mathematical representations.

**Word Problem Example #1**

(1) In a taste test 50 fewer people preferred Pepsi to Coke.

**by Patrick Bennett, St. Mary's High School**

x+8

**Mathematical Symbols**

3(x+8)

z-5

A number plus eight.

Eight more than a number.

Three times the sum of a number and eight.

A number minus five.

Five less than a number.

The difference of a number and five.

Mathematical Symbols

Words

Examples

a number

more than

plus

the sum of

five

A number minus three.

The difference between a number and three.

Three less than a number.

minus

the difference between

less than

a number

three

The product of a number and 2.

Twice a number.

Two times a number.

or

2y

Five more than a number.

A number plus five.

The sum of a number and five.

z - 3

Two

Twice

The product of

Twice

times

a number

2 • y

How to translate word phrases into math phrases.

=

78

More examples....

Three less than the number x equals forty-four.

x - 3 = 44

Four times the sum of a number and seven is 92.

4(x + 7) = 92

If two times a number decreased by six is divided by eight, the result is sixty-one.

2x - 6

8

= 61

In this lesson we will study how to translate written-word descriptions of mathematical situations into math problems.

Let's first recall what we discussed in a previous lesson: mathematical symbols.

Notice here we have translated mathematical symbols into written-word descriptions of mathematical situations.

In order to begin mastering the dreaded "word problem", all we need to do is *work in reverse*, from the words back to the symbols!

(1)

pepsi = coke - 50

(2)

pepsi + coke = 300

(c - 50) + c = 300

p = ?

c = ?

Word Problem Example #2

(1) Nora drove 5 miles less than half the distance Kaelani drove.

k = ?

(1)

norah = kaelani - 5

1

2

(2)

kaelani = norah + 30

k = ( k - 5) + 30

1

2

Remember: the goal is to arrive at a single equation with a single variable/unknown that will enable us to answer the "find" question.

Almost all the word problems we cover in Algebra will contain 2 statements and a question.

Here's an example:

(1) In a taste test 50 fewer people preferred Pepsi to Coke.

(2) 300 people participated in the taste test.

How many people preferred each?

By translating the statements into mathematical symbols, we can create the single equation we need to answer the question.

(2) 300 people participated in the taste test.

p = c - 50

p + c = 300

How many people preferred each?

p = c - 50

p + c = 300

c - 50 + c = 300

2c - 50 = 300

2c = 350

c = 175

*

p = c - 50

p = 175 - 50

p = 125

*

125 people preferred Pepsi,

and 175 people preferred Coke.

How far did Kaelani drive?

(2) Kaelani drove 30 miles further than Nora.

n = k - 5

1

2

k = n + 30

n = k - 5

1

2

k = n + 30

k = k - 5 + 30

1

2

k = k + 25

1

2

k = 25

1

2

k = 50

*

Kaelani drove 50 miles.

(2)

(1)

5 Step Word Problem Solving Plan

1) Read problem carefully. Translate each sentence into math symbols. Create a Formula Chart, and/or sketch a picture or diagram to help organize and visualize information in complex word problems.

2) Choose variables to represent the unknowns.

3) Use substitution to create 1 equation with 1 variable.

4) Solve the equation. Check the question sentence and use solution to find what was asked for. Write answer as a complete sentence.

5) Reread the problem. Check your work. Be sure you have found what was asked for by the question sentence.