1. Applications of Linear Equations
Example 1:
Joe’s age is 5 less than Fred’s age. Their combined age is 71 years. Find Joe’s age.
1) Variable declaration:
Joe’s age is described in terms of Fred’s age.
Let x represent Fred’s age.
Let x - 5 represent Joe’s age (5 less).

2. Joe’s age is 5 less than Fred’s age. Their combined age is 71 years
Joe’s age is 5 less than Fred’s age. Their combined age is 71 years. Find Joe’s age.
x = Fred
2) Write the equation:
x - 5 = Joe
combined age means add
(Joe’s age) + (Fred’s age) = 71 years

3. Joe’s age is 5 less than Fred’s age. Their combined age is 71 years
Joe’s age is 5 less than Fred’s age. Their combined age is 71 years. Find Joe’s age.
3) Solve the equation:

4. Joe’s age is 5 less than Fred’s age. Their combined age is 71 years
Joe’s age is 5 less than Fred’s age. Their combined age is 71 years. Find Joe’s age.
4) Write an answer in words, explaining the meaning in light of the application
x = Fred
x - 5 = Joe
Joe’s age is 33 years.
Fred’s age is 38 years.

5. Applications of Linear Equations
Example 2:
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.

6. 1) Variable declaration:
Make a drawing of a board:
Cut the board into pieces
Short
Middle
Long

7. A 5 foot board is cut into three pieces
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.
Short
Middle
Long

8. A 5 foot board is cut into three pieces
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.
Short
Middle
Long
Note that all lengths are written in terms of the shortest piece. Let the length of the short piece be x.

9. A 5 foot board is cut into three pieces
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.
Short
Middle
Long

10. A 5 foot board is cut into three pieces
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.
Short
Middle
Long
24 inches longer …
than 3 times the shorter …

11. A 5 foot board is cut into three pieces
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.
Short
Middle
Long
6 inches less than …
twice the shortest …

12. A 5 foot board is cut into three pieces
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.
Short
Middle
Long
The board is 5 feet long. Since the long piece was given in terms of inches, convert the 5 feet to inches.

13. Short
Middle
Long
2) Write the equation:
(short) + (middle) + (long) = total length

14. Short
Middle
Long
3) Solve the equation:

15. 4) Write an answer in words, explaining the meaning in light of the application
Short
Middle
Long

16. Short
Middle
Long
Short piece length = 7 inches
Middle piece length = 8 inches
Long piece length = 45 inches
Note that the lengths add up 60 inches, the total length of the board.

17. The long piece is 45 inches.
Look at the given problem again to determine exactly what was asked for:
A 5 foot board is cut into three pieces. The longest piece is 24 inches longer than three times the shortest piece. The middle piece is 6 inches less than twice the shortest piece. Find the length of the long piece.
The long piece is 45 inches.

18. END OF PRESENTATION