MATH 1090.004 College Algebra for Business and Social Science (3 credits)
Instructor: Laura Strube
Chapter 1.3 and 1.4 Word Problems and Examples
1. Jorge is going bowling by himself. The cost of his bowling will be $2.00 to rent a pair of
shoes and then the $1.50 for each game he bowls. Write a linear equation which shows
how much the bowling will cost Jorge if he bowls x games. Then identify the slope and
y-intercept of this equation and explain what it means.
Solution:
Remember from lecture, we have three possible cases:
1. Case 1 - Given: slope and y intercept
2. Case 2 - Given: slope and point
3. Case 3 - Given: two points
Step 1: Determine Unknowns
In this problem we have two unknowns:
• The number of games played
• The total amount of money Jorge paid for bowling
We would like to be able to “input” the number of games played and “output” the
total cost. So we will let:
• x = number of games played (independent variable)
• y = total cost (dependent variable)
Step 2: Determine the case of the problem
• We are told that it costs Jorge to $2.50 rent a pair of shoes. Thus it costs Jorge
$2.50 to play zero games. We represent this fact as the point: (0, 2.50).
• Were are told that it costs Jorge $1.50 per game. The word ”per” tells us we are
talking about slope. We are given money per game so the slope is:
m=
change in y
change in x
= 1.5 = 23 .
So, we see that this problem is a word problem of case (1).
Step 3: Find the equation
We will use the Slope - Intercept Formula: y = mx + b
Plug in our facts:
y = mx + b
3
Solution: y =
x + 2.5
2
2. Water freezes at 32◦ F which is 0◦ C. Water boils at 212◦ F which is the same as 100◦ C.
What Celcius Temperature corresponds to 70◦ F? Write a linear equation that fits this
data.
Solution:
Step 1: Define the variables:
• x = temperature in Fahrenheit (independent variable)
• y = temperature in Celsius (dependent variable)
Step 2:Find the Points
Observe that we are given two points:
• (x1 , y1 ) = (32, 0)
• (x2 , y2 ) = (212, 100)
Step 3: Determine Case
Since we are given two points this is a case (3) problem.
Step 4: Find the Equation
• First we have to find the slope: m =
y2 −y1
x2 −x1
=
100−0
212−32
=
100
180
=
5
9
• Choose a point: we choose (32,0) [It doesn’t matter which point we choose]
• Find the equation:
We use the point slope formula: (y − y1 ) = m(x − x1 )
(y − y1 ) = m(x − x1 )
5
(y − 0) =
(x − 32)
9
5
7
y =
x − 17
9
9
• Find the Celsius temperature that corresponds to 70◦ F
y = 95 (70) − 17 79 = 21 19