Word Problems 1 Name

Word Problems 1 Name:

Consecutive Integers

Let’s work on some classic algebra word problems! Remember: Algebra exists to help us solve problems that you can’t solve in your head. You should always start a problem by trying to figure it out without algebra. If you can’t solve it that way, then algebra will come to your rescue!

Try this problem in your head:

Three positive consecutive integers have a sum of 9. What are the three integers?

Now try this problem. This is a trickier problem!

Five consecutive even integers have a sum of 10. What are the integers?

Algebra helps us solve trickier problems like the one above. Let’s see how it works.

Find the pattern and fill in the blank:

Consecutive Integer / Consecutive Even Integer / Consecutive Odd Integer
2, 3, ______, 5
-4, -3, -2, ______/ 6, 8, ______, 12
-16, ______, -12, -10 / 11, 13, ______
-19, ______, -15
How can we write an expression for four consecutive integers?
Let x = 1st integer / How can we write an expression for four consecutive even integers? / How can we write an expression for three consecutive odd integers?

Try these!

1) If x +3 represents an integer, then the next consecutive integer in terms of x is

(1) x (2) x +2 (3) x +4 (4) x +5

2) If x - 4 represents an odd integer, then the next consecutive odd integer in terms of x is

(1) x - 6 (2) x - 4 (3) x - 3 (4) x – 2

3) If n - 6 is an even integer, what is the next larger consecutive even integer?

Follow the leader: Look at each example below. Then try a problem that is like it.

Leader: Find two consecutive integers whose sum is 95
Define Variables:
Let n = the first integer.
Let n + 1 = the second integer
Equation:



Answer: The two consecutive integers are 47 and 48. / You: Find two consecutive integers
whose sum is 33.
Define Variables:
Equation:
Answer:______
Leader: Find three consecutive odd integers whose sum is 45
Define Variables:
Let n = the first integer.
Let n + 2 = the second integer
Let n + 4 = the third integer
Equation:

Continue solving / You: Find two consecutive odd integers whose
sum is 36.
Define Variables:
Equation:
Answer:______