Games
Problems
Go Pro!

# Pairs of Consecutives

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems

## Pairs of Consecutives

The sum of two pairs of consecutive integers is 100. the difference between the largest and the smallest of these four integers is 9 less than the average of the four integers.

Find all four integers.

Presentation mode
Problem by madelynK

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Assign this problem
Click here to assign this problem to your students.

## Similar Problems

### Antique Table Price

The price of an antique table varies directly with age of the antique (in years) and with the surface area (in square feet). The price varies inversely with the number of scratches on the surface.  A table which is 120 years old, is 3 feet x 8 feet , and has n scratches on the surface, costs \$4,320. A table which is 140 years old, is 4 feet x 8 feet, and has n - 1 scratches on the surface, costs \$7,680.  If a table 150 years old, which is 4 feet x 6 feet , costs \$10,800, how many scratches are on the surface?

### Math Textbooks for Sale

The cost of a textbook is directly proportional to the number of math problems it contains, and inversely proportional to the number of authors who wrote the book. A textbook which contains 200 problems, and was written by 3 authors costs \$5 less than a textbook which contains 150 problems, and was written by 2 authors. What is the cost of a textbook containing 450 problems, and written by 4 authors?

### Six more than Twice the Smaller

The sum of two numbers is six more than twice the smaller number, and if the larger number is multiplied by three, the result is ten less than seven times the smaller number. What is the larger number?

### Manny Climbs a Skyscraper

Manny is climbing to the top of skyscraper, starting from the ground floor (Floor #1). There are 12 steps between each floor. When he reaches the landing for the nth floor, the number of floors he has left to climb is equal to a quarter of the number of steps he's already climbed. When he reaches the landing for the kth floor, the number of floors he has left to climb is equal to one sixth the number of steps he's already climbed.

When Manny has climbed halfway to the top of the skyscraper, the number of steps he has climbed is a three digit number, with the digits in descending order from left to right.

If the skyscraper has at least 40 floors, and no more than 110 floors, how many stairs does Manny climb in all?

### Three Digits by Sums

I am a three digit number. The sum of my first two digits is 15, and the sum of my last two digits is 8. The sum of my first and last digits is 7. What number am I?

### Henry's Books

Henry has five books. The third book has 100 fewer pages than the first and second books combined. The fourth book has 50 pages more than twice the number of pages in the first book. The last book has 150 fewer pages than three times the second book. In all, his books have 748 pages.  Together, his first and second books have 216 pages. How many pages does his largest book have?

### Handshakes

Mr. T wants each of his math students to shake hands with each of his other math students exactly once. He also wants each of his math students to shake Mr. H's hand twice. Mr. T shakes Mr. H's hand once. If there were 78 handshakes in all, how many math students does Mr. T have?

### Difference System

The difference between two numbers is twice the smaller number. The smaller number is 10 less than the larger number. Find the smaller number.

### A Sum of Sums

If the sum of an integer and the next consecutive integer is added to the sum of another integer and its next consecutive odd integer, the result is 71.

If the smaller of the two numbers is subtracted from twice the larger, the result is 29.  What are the two numbers?

### Difference and Sum

Two numbers add to twenty-seven more than the opposite of the smaller number. The numbers differ by three. What is the larger number?

Chickens and Roosters, X to Y to Z, Sum and Difference, Triangle Perimeter, Coffee and Donuts, Sum of Two Fractions, Napkins, Forks, and Plates, Humpty Dumpty, Spiders and ants, Bag of Candy

# Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
The text passage contains multiple math problems, each presented as a word problem. Each problem is a system of equations or a single equation that needs to be solved to find the answer.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Games
Problems
Go Pro!

# Pairs of Consecutives

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems

## Pairs of Consecutives

The sum of two pairs of consecutive integers is 100. the difference between the largest and the smallest of these four integers is 9 less than the average of the four integers.

Find all four integers.

Presentation mode
Problem by madelynK

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Assign this problem
Click here to assign this problem to your students.

## Similar Problems

### Antique Table Price

The price of an antique table varies directly with age of the antique (in years) and with the surface area (in square feet). The price varies inversely with the number of scratches on the surface.  A table which is 120 years old, is 3 feet x 8 feet , and has n scratches on the surface, costs \$4,320. A table which is 140 years old, is 4 feet x 8 feet, and has n - 1 scratches on the surface, costs \$7,680.  If a table 150 years old, which is 4 feet x 6 feet , costs \$10,800, how many scratches are on the surface?

### Math Textbooks for Sale

The cost of a textbook is directly proportional to the number of math problems it contains, and inversely proportional to the number of authors who wrote the book. A textbook which contains 200 problems, and was written by 3 authors costs \$5 less than a textbook which contains 150 problems, and was written by 2 authors. What is the cost of a textbook containing 450 problems, and written by 4 authors?

### Six more than Twice the Smaller

The sum of two numbers is six more than twice the smaller number, and if the larger number is multiplied by three, the result is ten less than seven times the smaller number. What is the larger number?

### Manny Climbs a Skyscraper

Manny is climbing to the top of skyscraper, starting from the ground floor (Floor #1). There are 12 steps between each floor. When he reaches the landing for the nth floor, the number of floors he has left to climb is equal to a quarter of the number of steps he's already climbed. When he reaches the landing for the kth floor, the number of floors he has left to climb is equal to one sixth the number of steps he's already climbed.

When Manny has climbed halfway to the top of the skyscraper, the number of steps he has climbed is a three digit number, with the digits in descending order from left to right.

If the skyscraper has at least 40 floors, and no more than 110 floors, how many stairs does Manny climb in all?

### Three Digits by Sums

I am a three digit number. The sum of my first two digits is 15, and the sum of my last two digits is 8. The sum of my first and last digits is 7. What number am I?

### Henry's Books

Henry has five books. The third book has 100 fewer pages than the first and second books combined. The fourth book has 50 pages more than twice the number of pages in the first book. The last book has 150 fewer pages than three times the second book. In all, his books have 748 pages.  Together, his first and second books have 216 pages. How many pages does his largest book have?

### Handshakes

Mr. T wants each of his math students to shake hands with each of his other math students exactly once. He also wants each of his math students to shake Mr. H's hand twice. Mr. T shakes Mr. H's hand once. If there were 78 handshakes in all, how many math students does Mr. T have?

### Difference System

The difference between two numbers is twice the smaller number. The smaller number is 10 less than the larger number. Find the smaller number.

### A Sum of Sums

If the sum of an integer and the next consecutive integer is added to the sum of another integer and its next consecutive odd integer, the result is 71.

If the smaller of the two numbers is subtracted from twice the larger, the result is 29.  What are the two numbers?

### Difference and Sum

Two numbers add to twenty-seven more than the opposite of the smaller number. The numbers differ by three. What is the larger number?

Chickens and Roosters, X to Y to Z, Sum and Difference, Triangle Perimeter, Coffee and Donuts, Sum of Two Fractions, Napkins, Forks, and Plates, Humpty Dumpty, Spiders and ants, Bag of Candy

# Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
user
The text passage contains multiple math problems, each presented as a word problem. Each problem is a system of equations or a single equation that needs to be solved to find the answer.

TYPE: MULTIPLE_QUESTIONS