SWBAT: solve word problems
Name: ____________________________________________________________ Date: ______________
Lesson 21
Word Problems Day 5
Warm Up
Mr. Jantzen bought some cans of soup at $0.39 per can, and some packages of frozen vegetables at $0.59 per package.
He bought twice as many packages of frozen vegetables as cans of soup. If the total bill was $9.42, how many cans of
soup did he buy?
Consecutive Integers
Consecutive Integers are integers that follow one another in order.
Example:
{2, 3, 4, 5}
{-9, -8, -7, -6}
Rule for Consecutive Integers:
Let x = 1st integer
Consecutive Even Integers are even integers that follow one another in order.
Example:
{2, 4, 6, 8, 10}
{-8, -6, -4, -2}
Rule for Consecutive Even Integers:
Let x = 1st integer
Consecutive Odd Integers are odd integers that follow one another in order.
Example:
{1, 3, 5, 7, 9}
{-9, -7, -5, -3}
Rule for Consecutive Odd Integers:
Let x = 1st integer
1
SWBAT: solve word problems
Check for understanding
1) If x + 3 represents an integer, than the next consecutive integer in terms of x is
2) If x – 4 represents an odd integer, then the next consecutive odd integer in terms of x is
3) If x + 2 represents an odd integer, then the next consecutive even integer in terms of x is
Consecutive Integers Word Problems
Example Set 1: Model Problem
(a) Find three consecutive integers whose sum is 45.
(b) Find four consecutive even integers whose sum is 36.
2
SWBAT: solve word problems
Practice Problems
1) Find three consecutive odd integers whose sum is 63.
2) Find two consecutive integers such that their sum is 89.
Example Set 2: Model Problem
(a) The sum of the ages of the three Romano brothers is 63. If their ages can be represented as consecutive
integers, what is the age of the middle brother?
3
SWBAT: solve word problems
(b) Find the second of three consecutive integers if the sum of twice the first and 4 times the second is equal
to eighteen less than the third.
Practice Problems
1) Find 4 consecutive even integers such that the sum of the smallest and 3 times the largest is 106.
2) Three sisters have ages that are consecutive odd integers. Find the ages if the sum of the age of the
youngest and three times the age of the oldest is five less than five times the middle sister’s age.
4
SWBAT: solve word problems
Regents Questions
3) The ages of three brothers are consecutive even integers. Three times the age of the youngest brother
exceeds the oldest brother's age by 48 years. What is the age of the youngest brother?
4) The sum of three consecutive odd integers is 18 less than five times the middle number. Find the three
integers.
Challenge - Reasoning
1. Explain why x and x + 1 cannot represent two consecutive odd integers.
2. Suppose that n and n + 1 represent two consecutive integers.
(a) Represent their sum in terms of n in simplest form.
(b) Explain why this sum must always be odd.
5
SWBAT: solve word problems
Summary
6
SWBAT: solve word problems
Name: ____________________________________________________________ Date: ______________
Word Problems Day 5
1) Find three consecutive odd integers that have an average of 13.
2) Find three consecutive even integers such that the sum of twice the first and three times the third is
fourteen more than four times the second.
3) Find two consecutive integers such that the larger is 8 less than twice the smaller.
7
SWBAT: solve word problems
4) Find three consecutive odd integers such that eight more than the sum of the first two is equal to eleven
less than three times the third.
5) Find three consecutive odd integers such that twice the sum of the first and third exceeds the second by
fifteen.
6) Find three consecutive integers such that the sum of twice the second and three times the third is five less
than six times the first.
8