Overhead Sheets
A. 1C
Writing equations &
inequalities
1
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
2
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.
3
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
4
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.
5
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.
6
Each month Jean’s phone bill includes a
$25 basic fee plus a charge of $.07 per
minute for the number of minutes of longdistance 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?
7
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
8
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
9
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
10
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
11
Grade 10 TAKS
A candy company sells chocolatecovered 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
12
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
13
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=¾x
B y=-¾x
C y=x-¾
D y=x+¾
14