Consecutive Integers

Linear Problems

Objective: Students will be able to solve consecutive integers problems.

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, …

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

Read and solve

Step 1:

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

number.

Step 2:

• Setup the Equation.–(x) + (x + 2) = -14

Step 3:• Solve the equation.

(x) + (x + 2) = -14

x + x + 2 = -14

2x + 2 = - 14

- 2 - 2

2x = -16

2 2

x = - 8

Step 4

• Answer the question

x = –8

x + 2 =

• Check

–8 + (–6) = –14

-6

Speed, Distance & Time

Speed, Distance, Time Calculations

The aim of this lesson is to be able to use the correct formulas to

calculate speed, distance or time

15 mins = 0•25 hourSo: 3 hours 15 mins = 3•25 hours

30 mins = 0•5 hourSo: 7 hours 30 mins = 7•5 hours

45 mins = 0•75 hourSo: 2 hours 45 mins = 2•75 hours

Reminder: How to change minutes into a decimal

The 3 formulas for Speed, Time & Distance:

Speed = Distance

TimeTime =

Distance

SpeedDistance =Speed x Time

Remember them from

this triangle:

D

S T

Solving for Speed Solving for Time Solving for Distance

D

S T

A windsurfer travelled 28 km in 1 hour 45 mins.

Calculate his speed.

Speed =

DistanceTime

28

1•75=

= 16 km/h

1 hour 45 mins

Answer: His speed was 16 km / hour

2 hour 30 mins

Answer: He travelled 125 km

A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel?

D

S TDistance = Speed x Time

= 50 x 2•5

= 125 km

Answer: It took 9 hours 15 minutes

A train travelled 555 miles at an average speed of 60 mph. How long did the journey take?

D

S TTime =

DistanceSpeed

55560=

= 9•25 hours

= 9 hours 15 mins