In the lesson on Algebraic
Representations we looked at writing mathematical
expressions.
We are ready now to write mathematical
equations.
Expressions:
10,
2 + y,
z,
7xy,
5x  6,
2(a + 3),
x^{2} + 4x
+ 4
"Expressions" do NOT have an equal sign. 

Equations:
2 + y = 10
5x  6 = 41
x^{2} + 4x + 4 = 0
"Equations" have an EQUAL sign. 


"Expressions"
and "equations" refer to two different entities in mathematics.
If you are dealing with an EQUAL SIGN, you are dealing with an
"equation".
EQUAtion ↔
EQUAL sign
An equation is a sentence where two algebraic expressions are
equal.

Translate the following problems into equations:
HINT: If you are having trouble determining what
the equation might be, make a numerical problem to see how the
numbers in the problem are related to one another.
1. 
Cost for cable TV service in a certain city is $45 for the
installation and $24 a month for service.
Number
problem: for 3 months the cost would be: Cost = $24
• 3 + $45. Replace 3 with m. 
Let c =
cost, m = number of months
c = 24m + 45

2. 
If golf balls cost $1.25 and
putters cost $79, how many of each can the golf team purchase for
$150?
Number
problem: if I purchase 2 golf balls and 3 putters the cost
will be: Cost = 1.25•2 + 79•3
Replace 2 with g (number of golf balls), 3 with p
(number of putters), and Cost with $150. 
Let g =
number of golf
ball,
p = number of putters
1.25g + 79p = 150

3. 
H_{2}O means that
water contains two hydrogen atoms and one oxygen atom.
Number
problem: In water, if there is one oxygen atom, there are
2 hydrogen atoms; if there are two oxygen atoms, there are 4
hydrogen atoms and so on. The number of hydrogen atoms is
twice the number of oxygen atoms. 
Let O =
number of oxygen atoms,
H = number of hydrogen atoms
H = 2O 
4. 
A cookie recipe calls for
twice as many chocolate chips as walnuts.
Number
problem: if a recipe calls for 10 walnuts, it calls for 20
chocolate chips. The number of chocolate chips is twice the
number of walnuts. 
Let c =
number of chips,
w = number of walnuts
c = 2w 
5. 
What is the total weight of a filled hot tub, if the
tub weighs 350 pounds and the water weighs 10 pounds per gallon?
Number
problem: if it takes 100 gallons to fill the hot tub, the
total weight will be:
Total = 10 • 100 + 350 Replace 100 with g, for the
number of gallons.. 
Let t =
total weight,
g = number of gallons
t = 10g + 350 
