Overhead Sheets



Overhead Sheets

A. 1C

Writing equations & inequalities

When we write equations or inequalities, we take the written description of a situation, and we represent that situation using mathematical symbols.

Example:

A boat is 40 times larger than its scale model. Write an equation to represent this relationship.

Step 1: Identify your variables

b = the size of the boat

s = the size of the scale model

Step 2: Write the equation

“boat is” can be represented by

b =

b = 40s

Practice writing equations for the following situations:

(a) Pencils cost $.35 each. Write an equation to calculate the total cost of any number of pencils.

(b) A motel charges $50 per night for a room. Write an equation to represent the charge for a stay at the hotel.

(c) Bananas cost $.39 per pound. Write an equation to calculate the cost of buying bananas.

In some math problems, we have one value which is a constant. That value does not change and does not depend on any other variable. We have other values which are dependent upon some other unit in the problem.

Example:

You hire an electrician to install a light in your kitchen. The electrician charges $68 for the house call, plus $50 an hour for service. Write an equation to represent the cost of hiring this electrician.

c = cost

h = # of hours

Write the equation

Name the constant

Practice:

(a) To rent a hotel room for one night, a company charges $85 plus $10 per person. Write an equation to calculate the total cost of staying at this hotel.

(b) The admission to a state park is $5.00 per vehicle plus $.50 per passenger. Write an equation to represent the total admission to the state park for your family.

Function Rule

An equation represents a functional relationship.

Sometimes we are asked to write a function rule instead of an equation.

A function rule is a special type of equation that uses f(x) to represent y.

In other words, instead of writing y =

you would write f(x) =

f(x) means “the value of the function at x”

Your independent variable would go inside the parenthesis. Sometimes that variable is “x”, sometimes is it some other letter.

Each month Jean’s phone bill includes a $25 basic fee plus a charge of $.07 per minute for the number of minutes of long-distance calls she makes. Write a function rule to describe the total amount of Jean’s monthly phone bill in terms of m, the number of minutes of long-distance calls she makes.

f(m) = 25 + 0.07m

How would you write this as an EQUATION?

Functional Notation

To write an equation in functional notation, we give the function a name, typically a letter such as f, g, or h. Then use an algebraic expression to describe the y-coordinate of an ordered pair.

Equation: y = 2x + 16

Functional notation: f(x) = 2x + 16

Equation: m = h – 2

Functional notation: f(h) = h – 2

On the TAKS, you will be asked to solve problems in which you must write an equation or inequality for a given situation.

Example: Grade 9 TAKS

The Alejo family budgeted $2000 for their vacation. Their budget consisted of $800 for travel costs and $75 per day for other expenses. Which inequality represents the number of days, x, the family could have stayed on vacation?

A 800 + 75x ≤ 2000

B 800x + 75 ≥ 2000

C 800x – 75 ≥ 2000

D 800 – 75x ≤ 2000

Grade 9 TAKS

The temperature in degrees Celsius, C, is 5/9 of the difference between the temperature in degrees Fahrenheit, F, and the constant 32. Which equation best represents this relationship?

A C = 5/9 – (F + 32)

B C = 5/9 (F + 32)

C C = 5/9 (F – 32)

D C = 5/9 – F + 32

Grade 10 TAKS

Vicki works as a salesclerk in a clothing store. She earns $10 per hour plus a commission of 6% of her total sales. Which equation represents e, her total earnings, when she works h hours and sells a total of d dollars in merchandise?

A e = 10h + 0.06d

B e = 10h + 0.6d

C e = 6h + 10d

D e = 0.06h + 10d

Grade 10 TAKS

A candy company sells chocolate-covered cherries in a box. The empty box weighs 4.2 ounces. Each piece of candy weighs at least 1.8 ounces. Which inequality best describes the total weight in ounces, w, of a box of chocolate – covered cherries in terms of c, the number of candies in the box?

A w ≥ 1.8c + 4.2

B w ≥ 1.8c – 4.2

C w ≥ 4.2c + 1.8

D w ≥ 4.2c – 1.8

Grade 11 TAKS

Eddie’s Towing company charges 440 to hook a vehicle to the tow truck and $1.70 for each mile the vehicle is towed. Which equation best represents the relationships between the number of miles towed, m, and the total charges, c?

A c = 40 + 1.70

B c = 40 + 1.70m

C c = 40m + 1.70m

D c = 40m + 1.70

Grade 11 TAKS

An artist studies human proportions in order to make realistic drawings. He observes that a person’s kneeling height, y, is ¾ of the person’s standing height, x. Which equation best represents this relationship?

A y = ¾ x

B y = - ¾ x

C y = x - ¾

D y = x + ¾

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