Math 251: Beginning Algebra
Section 4.4 Notes
Solving an Applied Problem with Two Variables
Step 1
Read the problem carefully until you understand what is given and what is to be found.
Step 2
Assign variables to represent the unknown values, using diagrams or tables as needed.
Write down what each variable represents.
Step 3
Write two equations using both variables.
Step 4
Solve the system of two equations.
Step 5
State the answer. Does it seem reasonable?
Step 6
Check the answer in the words of the original problem.
Example 1: Two top-grossing Disney movies in 2002 were Lilo and Stitch and The Santa Clause 2.
Together they grossed $284.2 million. The Santa Clause 2 grossed $7.4 million less than Lilo and
Stitch. How much did each movie gross?
Step 1
Step 2
Read
Assign variables
Step 3
Write two equations
Step 4
Solve
Step 5
Step 6
State the answer
Check
Math 251: Beginning Algebra
Section 4.4 Notes
Example 2: In 1997-1998, the average movie ticket (to the nearest U.S. dollar) cost $10 in Geneva
and $8 in Paris. If a group of 36 people from these two cities paid $298 for tickets to see The Rookie,
how many people from each city were there?
Step 1
Step 2
Read
Assign variables
Step 3
Write two equations
# of Tickets
Step 4
Solve
Step 5
Step 6
State the answer
Check
Price per ticket
Total value
Math 251: Beginning Algebra
Section 4.4 Notes
Example 3: How many liters of a 25% alcohol solution must be mixed with a 12% solution to get
13 L of a 15% solution?
Step 1
Step 2
Read
Assign variables
Step 3
Write two equations
25%
12%
+
% Concentration
of alcohol
Step 4
Solve
Step 5
Step 6
State the answer
Check
15%
=
Liters of
Solution
Liters of pure alcohol
Math 251: Beginning Algebra
Section 4.4 Notes
Water/Air Current Problems:
x = speed of the boat in still water (speedometer reading)
y = speed of the current
r = true rate of the boat
x
x
y
y
Downstream (with current)
r=x+y
Upstream (against current)
r=x–y
Example 4: In one hour, Abby can row 2 mi against the current or 10 mi with the current. Find the
speed of the current and Abby’s speed in still water.
Step 1
Step 2
Read
Assign variables
Step 3
Write two equations
Rate
Step 4
Solve
Step 5
Step 6
State the answer
Check
Time
Distance