Consecutive Integers

1
Consecutive Integers

• Linear Problems

2
Do now

• 1) 2x 12 x 2
• 2) x (x 1) 27

3
Problem of the day

• Three brothers share the same birthday. James is
  the youngest, Jamaal is the oldest, while John is
  the middle brother. Their ages can be
  represented by 3 consecutive numbers whose sum
  equals 60. What are their ages?

Students will be able to solve consecutive
integers problems.
4
Solution

• Let
• x the youngest brother
• x 1 the middle brother
• x 2 the oldest brother
• Setup an equation
• x (x 1) (x 2) 60

Students will be able to solve consecutive
integers problems.
5
Solution Cont

• Solve the equation
• x (x 1) (x 2) 60
• x x 1 x 2 60
• 3x 3 60
• - 3 - 3
• 3x 57
• 3 3
• x 19

Students will be able to solve consecutive
integers problems.
6
Solution Cont

• Answer the Question!
• x 19
• x 1
• x 2
• James is 19 years old
• Jamaal is 20 years old
• John is 21 years old

20
21
Students will be able to solve consecutive
integers problems.
7
Demo 2

• The sum of two consecutive even numbers is -14.
  What are the two numbers.

Students will be able to solve consecutive
integers problems.
8
Step 1

• Define the unknown.
• Let x 1st consecutive number.
• Let x 2 2nd consecutive number.

Students will be able to solve consecutive
integers problems.
9
Step 2

• Setup the Equation.
• (x) (x 2) -14

Students will be able to solve consecutive
integers problems.
10
Step 3

• Solve the equation.
• (x) (x 2) -14
• x x 2 -14
• 2x 2 - 14
• - 2 - 2
• 2x -16
• 2 2
• x - 8

Students will be able to solve consecutive
integers problems.
11
Step 4

• Answer the question
• x 8
• x 2
• Check
• 8 (6) 14

-6
Students will be able to solve consecutive
integers problems.
12
Two Cases for Consecutive Numbers

• Case one
• Consecutive numbers like 4, 5, 6,7,
• x, x 1, x 2, x 3,
• Case Two
• Consecutive odd numbers like 5, 3, 1, 1, 3,
• x, x 2, x 4, x 6,
• Consecutive even numbers like 4, 2, 0, 2, 4,
• x, x 2, x 4, x 6,

Students will be able to solve consecutive
integers problems.
13
Summary

1. Define the variable (unknown)
2. Setup an equation
3. Solve the equation
4. Answer the question
5. Check your answer

Students will be able to solve consecutive
integers problems.