Transcript Problem Solving with Systems of Equations in Two and Three

Problem Solving with Systems of
Equations in Two and Three
Variables
Advanced Math Topics
Mrs. Mongold
Steps to writing a system of equations
 1. Read and re-read the problem
 2. Identify what it is you are trying to solve for
 3. Translate the words into variables
 4. Write an equation to model all of the situations
(2 variables, 2 equations, 2 situations, 3
variables, 3 equations, 3 situations)
 5. Solve the system
 6. Check your solution to make sure it makes
sense in terms of the problem (positive numbers
where positive numbers are required)
 7. Write your answer in sentence form!!!
Example 1
A first number is 4 less than a second
number. Four times the first number is 6
more than twice the second. Find the
numbers.
Example 2
Two cars leave Indianapolis, one traveling
east and the other west. After 3 hours
they are 297 miles apart. If one car is
traveling 5 mph faster than the other, what
is the speed of each?
Example 3
Lynn Pike, a pharmacist, needs 70 liters of
a 50% alcohol solution. She has available
a 30% alcohol solution and an 80%
alcohol solution. How many liters of each
solution should she mix to obtain 70 liters
of a 50% alcohol solution.
Example 4
A manufacturing company recently
purchased $3000 worth of new equipment
to offer new personalized stationery to its
customers. The cost of producing a
package of personalized stationery is
$3.00 and it is sold for $5.50. Find the
number of packages that must be sold for
the company to break even.
Example 5
The measure of the largest angle of a
triangle is 800 more than the measure of
the smallest angle, and the measure of the
remaining angle is 100 more than the
measure of the smallest angle. Find the
measure of each angle.
Example 6
The measure of the largest angle of a
triangle is 900 more than the measure of
the smallest angle, and the measure of the
remaining angle is 300 more than the
measure of the smallest angle. Find the
measure of each angle.
Homework
Day 1: pg 243-245/ 1,2,4,8,12,17,20,23,
24, 25, 30, 32, 36
Day 2: pg 246-247/ 40-46, 52