Overhead Sheets Writing Equations and Inequalities

Overhead Sheets
A. 1C
Writing equations &
When we write equations or inequalities,
we take the written description of a
situation, and we represent that situation
using mathematical symbols.
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 = 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
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.
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
(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
Function Rule
An equation represents a functional
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
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
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
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 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
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
A y=¾x
B y=-¾x
C y=x-¾
D y=x+¾