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 6, 8, ______, 12 11, 13, ______

-4, -3, -2, ______-16, ______, -12, -10 -19, ______, -15

How can we write an expression How can we write an expression How can we write an expression for four consecutive integers? for four consecutive even for three consecutive odd Let x = 1st integer integers? 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 You: Find two consecutive integers is 95 whose sum is 33.

Define Variables: Define Variables:

Let n = the first integer.

Let n + 1 = the second integer

Equation: Equation: n  n 1  95

2n 1  95 1 1 2n 94  2 2

n  47 n 1  48 Answer: The two consecutive integers are 47 and Answer:______48. Leader: Find three consecutive odd integers whoseYou: Find two consecutive odd integers whose sum is 45 sum is 36.

Define Variables: Define Variables:

Let n = the first integer.

Let n + 2 = the second integer

Let n + 4 = the third integer Equation:

Equation: n  n  2  n  4  45

3n  6  45 Continue solving Answer:______