1. Solving Application Problems
Friday
Solving Application Problems
Tuesday
Quiz #3
Thursday
In Class Test Review
Monday
UNIT 6 Test

2. Friday: Announcements
Calculator #18 missing?
Last topic for Unit 6 today
Quiz next class over applications
Unit 6 Quiz Corrections (3 quizzes) due on Test Day (Optional)

3. Solving Systems of Equations Applications (Word Problems)

4. Objectives I can write a system of equations from a word problem
I can write a system of inequalities from a word problem
I can solve for word problems with matrices

5. Word Problems Highlight the key information
Assign variables to represent the unknown values
Write equation to reflect the information provided. Look for key words and numbers.

6. Word Problems When solving a word problem, consider these suggestions
1. Identify what the variables are in the problem
2. Write equations that would represent the word problem, looking for key words
Sum, difference, twice, product, half, etc…

7. “Most” Problems Have 1 equation based on QUANTITY
Have 1 equation based on MONEY or VALUE
Can have a 3rd equation based on quantity comparison

8. Common Formulas
Perimeter of a shape (Rectangle, triangle, square, etc…)
Area of a shape
Some are provided on your notes handout

9. Coin Values in terms of a dollar
Quarter = $.25
Dime = $.10
Nickel = $.05
Penney = $.01

10. Example 1
Melissa has 57 coins in dimes and nickels. The total value of the coins is $4.60. How many coins of each kind does she have?
Nickels (N)
Dimes (D)
Equations:
N + D = 57
5N + 10D = or .05N + .1D = 4.60

11. Problem #2
At a pizza shop, two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas and a liter of soda cost $16. What is the cost of each item sold separately?

12. Problem #2 Solution
At a pizza shop, two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas and a liter of soda cost $16. What is the cost of each item sold separately?
Assign variables:
P – small pizza; L – liter of soda; S- salad
Now write equations:
2P + 1L + 1S = 14
1P + 1L + 3S = 15
3P + 1L = 16
Solution: (5, 1, 3)

13. Example 3
Given the following 3 ordered pairs of a parabola graph, write a system of equations for the 3 points and find the solution to write the quadratic equation in the format:
y = ax2 + bx + c
(-4, 30), (2, -18), and (3, -40)

16. Inequality Key Words

17. WS 6-7A Let’s complete the first 3 of WS 6-7A in class together.
The other 2 are part of homework

18. Homework
Worksheet 6-7 and finish 6-7A
Quiz next class

19. Example 3
At a recent movie, adult tickets were $4.50 and student tickets were $2.50. During opening night a total of 300 tickets were sold earning $ How many of each ticket type were sold?
Adult Ticket (A)
Student Ticket (S)
Equations:
A + S = 300
4.50A S = 1130

20. Example 7
Rental car agency A charges $8 per day plus $.20 per mile. Rental car company B charges $10, but only $.10 per mile. At what mileage is it better to use Company B?
Cost (C)
Miles (M)
Equations:
C = M
C = M