Application of Linear Equations

​Application of Linear Equations

Applied Math

Use linear Equations to solve problems

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Write an equation given a sentence​

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Solve a formula for a variable.

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​WHAT WILL I LEARN TODAY???

​Objectives

​Problem Solving with Linear Equations

​Strategy for solving word problems

1. Read e problem carefully

2. Write the expression for any other unknown quantities in terms of x

3. ​ Write an equation in x that models the verbal conditions of the problem.

4. Solve the equation

5. Check the solution​

Some text here about the topic of discussion

​Sum in all

More than

added,

plus

all together

Increased by​

​​Words

​decrease(d)

subtract take away

minus less than

difference

subtract

deduct ​

​

​​Words

times

product

of

twice by

double​

​area

​

​​Words

​divided

quotient

reciprocal

half of

goes into​

​​Words

​

Match

Match the following

• Sum

• Minus

• Product

• Quotient

Addition

Subtraction

Multiplication

Division

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Which operation is associated with this sentence

The sum of a number and 7

• Addition

• Subtraction

• Mulitplication

• Division

Multiple Choice

Which expression represents this sentence

A number decreased by 9

• n + 8

• n - 8

• n x 8

• n / 8

Multiple Choice

Which equation represents this sentence

The difference between a number and 8 is 12

• n + 8 = 12

• n /8 = 12

• n - 8 = 12

• n x 8 = 12

Multiple Choice

Which of the equations represents this sentence

The quotient of a number and 7 is 2

• $$\frac{n}{2}=7$$  

• $$n\ -7\ =\ 2$$  

• $$\frac{n}{7}=\ 2$$  

• $$n\ x\ 7\ =\ 2$$  

​Application of Linear Equations

​The median salary of a business major is more than that of a psychology major by $8 thousand as shown on the graph.

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The median salary of an English Major also exceeds a psychology major by $3 thousand

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Combined their median starting salaries are $116.​

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​Application of Linear Equations

​Determine the median starting salary of psychology, business and English Majors with bachelors degrees.

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Step 1: let x represent one of the unknown quantities

​x = median salary of psychology major

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Step 2 Represent the other unknown quantities​

​Business is 8 so x + 8 = median salary business.​

English is 3 so x + 3 = median salary of English Majors​

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Step 3: ​Write an equation in x that models the condition

​x + x + 8 + x +3 = 116

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Step 4: Solve for x

Combine like terms 3x + 11 = 116 subtract 11 3x = 105 divide by 3 x = 35 ​

​

​

​psychology majors $35,000

Business majors 35 + 8 = $43,000

English Majors 35 + 3 = $38​,000

​Final STEP!!! Check your answers

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35 +43 + 38 = 116 ​

Which year will college freshman be considered​ "being well off financially" essential or very important?

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​Step 1: let x represent unknown

x = number of years

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Step 2 represent unknown quantities

There are none so we can skip this one.

​​

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Which year will college freshman be considered​ "being well off financially" essential or very important?

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​Step 3: Solve for x

42 + 0.9x = 100

-42 -42

0.9x = 58 Divide by .9 to both sides

x = 64.4 which is 64 years​

​​

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​Final STEP!!! Check your answers

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42 + 0.9(64) = 100

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99.6 ≈​ 100

close enough​

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​Solving a Formula for One of It's Variables

​P = 2l + 2w Let's solve for w.

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P = 2l + 2w What do we need to do to isolate the w​?

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p-2l =2l -2l + 2w Subtract 2l from both sides

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p-2l = 2w​ Divide by 2 to both sides

​ 2 2

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p-2l = w is your FINAL result!

​ 2

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Solve for p​

T = D + PM

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p = ?​